Hello, I wrote this answer in response when a very similar question to yours was asked here:

The Bayeux Tapestry was started fairly soon after the battle itself and likely finished in the 1070s. It was instigated on the orders of William I's half-brother, Bishop Odo, who was present at events in Normandy preceding the battle, and during the battle itself. To that extent, it's heavily based on direct witness testimony, rather than on some kind of handed-down tradition, although is still clearly stylised. As you surmised, the Bayeux Tapestry is one of several roughly contemporaneous sources, all of which record the events surrounding the battle and then the conquest itself. By the standards of the period, the events of 1066 are recorded in quite exacting detail, largely because many of the chroniclers were present during the events, or heard from those who were. Our chief literary sources include William of Poitiers' Gesta Guillelmi, William of Jumièges' Gesta Normanorum Ducum, Guy of Amiens' Carmen de Hastingæ Proelio and the good old Anglo-Saxon Chronicle.

Broadly speaking the Bayeux Tapestry lies in accordance with the events recorded in those texts. There is debate around Harold's exact fate - stitching shows that the arrow striking him may have been an edit - but broadly speaking it's held in high regard. It's interesting to note that blinding had been a punishment under both Anglo-Saxon and Norman precedent for treason. Æthelred II, for example, has the eyes of the son of a treacherous noble put out, and his own son Ælfred was blinded on the orders of Harold's father Godwine when he tried to seize the throne following Cnut's death in 1035. Having Harold be blinded in this narrative, therefore, would make an important moral point about his treason to William, having previously made an oath to support him. Within the narrative of 1066, this serves to change Harold's actions from those of a questionably rightful heir defending against a foreign invader, to those of a treasonous usurper defying the true heir to the kingdom.

It's these perspectives that make the Bayeux Tapestry such an important and significant source for historians. Even if we can't necessarily 100% trust its version of events (and honestly even that' better than no accounts), the tapestry itself as an artefact tells us so much. It tells us of the political ambitions of the Normans, the ways in which they saw themselves and the means by which they sought to justify their rule. It tells us of their complex relationship with the English: Edward the Confessor is shown as a powerful and mighty king, the English - including Harold - are shown as brave and capable warriors, and the tapestry doesn't shy away from showing us the Norman dead being piled up by the English shield wall, or the fury of huscarls hacking apart charging knights. The tapestry tells us of the weapons, equipment and tactics of the Normans and the English: the extent to which chainmail was worn, the types of shields and swords, how the English formed their shieldwall and how it was used both to the front and overhead, how huscarls favoured axes, fought ahead of the line, and the damage they could do, how precisely the Normans fought on horseback.

The Tapestry gives us a great deal of information on appearance: it shows us the court robes worn by monarchs, the English fashion for tunics and the riding gear favoured by the Norman elite. It illustrates the Norman preference for closely-cropped hair and clean-shaven faces contrasted with the English fashion for long hair and luxuriant beards and moustaches. The Tapestry also shows us the veneration of relics, the style of reliquaries, their storage and transport, and how they are used in secular activies like the making of oaths. More prosaically, the Tapestry itself also shows us the materials, skills and influences of the English textiles industry and also tells us about methods of public display, contemporary types of decoration, and the importance of propaganda to early medieval kingship. Even if, therefore, we dispute the narrative of the Bayeux Tapestry - which is largely corroborated in contemporary literary sources, albeit with certain caveats re: arrows and oaths - the tapesty as a visual source is still hugely important and useful and a source.