It's an incredibly complex subject with its own technical jargon and obscure rules. From an English historiographical perspective the study of heraldry remained a largely antiquarian and professional pursuit until Maurice Keen turned his attention to the subject.

Military insignia are ancient (I can't give a precise date). According to Maurice Keen heraldry developed in response to the requirements of medieval warfare and armour (which covered the face and features of the individual in the melee, particularly in the tournament, where it was essential to know who one had unhorsed and thus who you might be taking prisoner) thus while before painted shields may have held only a decorative purpose they now served a particular function. See Chretien de Troyes' The Knight of the Cart for this in action.

Heraldic devices then began to be used on the surcoat, horse trappings, the nobility's seals, and depicted on tombs and effigies. This meant that these symbols took on a more significant aspect. They became hereditary to particular families, with clearly defined rules about how they could be presented. Our earliest examples are restricted to the highest and most powerful families whose power and possessions separated them from the 'ordinary knighthood'. For example, in the early twelfth-century Geoffrey the Fair wore a blue shield about his neck painted with golden lioncels. These same (six) golden lioncels on a blue shield could be found on Geoffrey's tomb in 1152. Geoffrey's bastard son William of Salisbury bore his father's device while his legitimate brother (also William) bore a single lion. This was the origin of the lion as a heraldic symbol of the Angevin family - and then would become part of the heraldic legacy of Normandy and England (and I'm sure other places where the Angevins settled - but do not quote me on that front).

Of course, when we discuss symbolism there is no need for them to have come with a pre-set meaning. Arms could as easily be used to create a new story as remember an old one. Thus the lions of England became incredibly important in the national mythos and the fleur-de-lis of France became representative of French royalists in the Hundred Years War (although this began under Philip IV, d.1314).

Arms were a serious business. The earliest heralds had begun distinct from heraldry. They were messengers and humble officials attached to armies (for example, they are described as waking the warriors before the battle of Las Navas de Tolosa, 1212). Heralds' precise purpose in cataloging those present at musters is unclear (as there is no evidence of knights being required to serve, or being paid for service, citing a herald's record as proof). Keen argues that this was ceremonious (creating precedence from those present) rather than practical in intention.

Sir Anthony Wagner (Garter King of Arms - ie. head of the College of Arms - an antiquarian and modern herald) argued that the heralds rise began with their role in the ceremony of the tournament. However, as we move beyond the twelfth- and thirteenth-centuries and into the later Middle Ages the herald came to serve important diplomatic functions. The role of arms also became more important. Heralds and heraldry developed their own unique law of arms. These laws could be used to resolve rare but verifiable incidents when two families bore the same arms. These were settled in the 'Court of Chivalry' (in England at least).

The Court of Chivalry and the profusion of documentation that it produced has not been a traditional topic of study, or typical resource, for historians and up until the Garter Kings of Arms A.R. Wagner and his successor George D. Squibb produced two fascinating examinations centred on the evidence so easily accessible to them at the College of Arms – yet lost to forgotten even by Garter Kings of Arms it would seem. Yet antiquarians had utilised the court records since the eighteenth century seeking to demonstrate the webs of connections and catalogue the disputes of the medieval and early modern elite. Until the work of Wagner and Squibb the Court of Chivalry had been entirely lost to historical research, in a strikingly similar decline to that of the court itself. The court is the only vestige of the civil law court that survived the reforms of the Victorians largely due to ‘the fact it never sat since the early part of the eighteenth century and so attracted no attention in the nineteenth.’ Indeed it was condemned in Parliament and its sittings ordered to cease in 1640. Squibb surmises that had the court been active it would have been subsumed into the secular jurisdictions ‘of all other courts in which the Advocates in Doctors’ Commons had formerly practices to the High Court of Justice created by the Supreme Court of Judicature Act, 1873.’ The College of Arms, which Squibb headed as one of three King of Arms, was founded by a royal charter in 1484 by Richard III the College of Arms was a royal corporation which professionalised the officers of arms under the three Garter Kings of Arms, though the college answers to the Earl Marshal of England. Yet even they, it seems, had forgotten the usage and existence of the Court of Chivalry, it was the Lord Mayor of Manchester, who caused the two century dormancy of the Court to be broken in 1954. Squibb produced his seminal discussion of the early modern cases of the court in 1959 which, in turn, revived interest in the court from medieval historians such as Maurice Keen and M.J. Russell.

Court of Chivalry was a civil court that pursued a mandate under the heading of armorial disputations. The most famous case of the medieval court was that between Sir Richard Scrope and Sir William Grosvenor. This seminal case set the precedent for the court’s jurisdiction. However, in later periods this was extended well beyond armorial disputes and became the favoured venue, until the Star Chamber usurped this role, of accusations of treason. ADD MS 35821 (British Library) details the accusations between Baron Thomas Morley and John Montacue, earl of Salisbury, and the ritual offering of proof by the body. While much of this is ritual, the offering of the gage for example, the intentions are startlingly real. The Court of Chivalry had become the last refuge of that perennially noble method of judgement: trial by battle. While in this instance the trial never came to blows, due to the death of one of the parties, it showcases the import which the medieval Court of Chivalry held. Keen argues that the existence and continued practice of the court was, in fact, unconstitutional with Clause 39 of Magna Carta, the right to be judged by one’s peers. The Court did, indeed, operate outside of the supposed rights of men in England, acting with royal authority based on letters patent but without the rights of indictment and jury. Yet the right to be tried according to the common law begs the question of whether the Court of Chivalry remained within the body of the common law or stood distinct from it as the Law of Arms. Squibb and his predecessors are convinced that it does yet Keen makes a compelling case for the Court to have operated not under the common law but under the distinct ‘law of arms’. Philologically this is a legitimate stance to take as the comments of Le Neve, Garter King of Arms, in the margins of ADD MS 35821, demonstrate that it was accorded to the law of arms that the two parties accused one another of treason and offered the gage. Moreover, the jurisdiction of the Court was ‘far from exclusive’ with cases of ransom and other ‘purely’ military matters come under the aegis of the constables court. Here again we see the importance of semantics, as Squibb is quite distinct in making the difference between the Constables Court, which could render judgement over a far wider range of disputes than that of the Court of Chivalry which was constricted largely to armorial disputes and those of the leaders of hosts. Here is Keen’s main divergence from Squibb where he correctly assesses Squibb’s divergence as being too narrow and that the distinction between the Constable’s Court and that of the Court of Chivalry was a false one. A famous case in 1386, where a duel was fought between Sir John Anneley and Sir Thomas Caterton took place, though this had expanded to disputes between member of the Order of the Garter by 1399 when Morley and Montacue were making accusations of treason against the realm. The chief distinction is the fact that the rights to court martial were shared between the officers of the army while the right to judge a case in the Court of Chivalry was reserved to the Marshal and Constable of England. This distinction is key for while ADD MS 35821 makes reference to the ‘law and customs of arms’ action is taken by ‘the constable considering by advice of marshal’.

Anyway, apologies - I'm getting tangential!

Here are some key sources:

The College-of-Arms still exists and has some fascinating info available.

Denholm-Young, N., History and Heraldry, Oxford, 1965.

Keen, M., Chivalry, London, 1984. | ‘Treason Trials Under the Laws of Arms’, Transactions of the Royal Historical Society, v.12 (December, 1962), 85-103. | ‘English Military Experience and the Court of Chivalry: The Case of Grey V. Hastings’, in Guerre et Société en France, en Angleterre et en Bourgogne XIV-XV siècle, eds. P. Contamine, C. Diry-Deloison and M. Keen, (1990), 123-142. | 'Chivalry, Heralds and History', in Knights, Nobles, and Men-at-Arms in the Middle Ages, London, 1996.

Squibb, G.D., The High Court of Chivalry: A Study of the Civil Law in England, Oxford, 1959.

Wagner, A.R., Heralds and Heraldry in the Middle Ages, Oxford, 1956.

Perhaps /r/heraldry could be of assistance.