The Great Wall is something I've covered in a few past answers, of which the most relevant is probably this one (hah! one /u/dankensington misssed), but I can write something that better contextualises the structure and its purpose.
The structure that we now know as the 'Great Wall of China' is the most prominent and best-preserved part of a system of defences established on the northern frontier of China by the Ming Empire (1368-1644/62), in response, ultimately, to the threat posed to the empire by nomadic peoples. The Ming had emerged out of a major revolt against the Mongols in the mid-14th century, but although the rulers of the Yuan Dynasty were successfully expelled from China itself, the Ming subsequently had great difficulty in turn projecting power into the steppe. While the Ming retained a degree of upper hand until the early 15th century, by the end of the 1420s the Ming had abandoned their forward strongholds in Mongolia, and over the course of the century they also found themselves having to fortify their northeastern frontier in Liaodong, where they had agricultural colonists in close proximity to the Jurchen tribes, who although nominally within the Ming orbit were nevertheless quite distinctly autonomous and occasionally aggressive. The resurgence of tribal power would be powerfully demonstrated in the Tumu Crisis of 1449, where Zhu Qizhen, the Zhengtong Emperor (r. 1435-49; 1457-64) was captured by an Oyirad (aka 'Western Mongol') army under Esen and held hostage. While the Ming tried to brush it off by deposing the now-kidnapped emperor and declaring his brother emperor in his stead, the shock to the system remained, and the Ming armed forces increasingly ceased to deem it possible to contend with steppe armies in field battles.
Increasing tribal raiding in the Ordos Plateau, a region which had always been heavily contested between sedentary and steppe powers, led the Ming to establish the first part of what might be termed the 'Great Wall' there in 1474, although this consisted more of a series of wall segments covering otherwise indefensible terrain than a single contiguous structure. Moreover, this covered only a small sector of the border, with the rest deemed safe enough given the presence of major fortresses, particularly those at Datong and Xuanfu to the northwest of Beijing, and the Jiayuguan in the Gansu Corridor. However, by the end of the 1530s the expansion of defensive works in these areas took higher priority as the targets of nomadic raids shifted eastwards. Based on Arthur Waldron's figures, some 42 new earthwork forts were built in the Datong area amid a surge of Oyirad activity between 1539 and 1560, and a further 6 would be built by 1570. The 1570s, in turn, saw an extensive overhaul of existing fortifications, with 43 earth forts reinforced with brickworks between 1572 and 1574 alone. Contemporary with these was the establishment of a new frontier wall covering the areas in front of Datong and Xuanfu as a first line of defence. In turn, raids shifted further eastwards, and by the 1560s walls were built covering the region north of Beijing. These walls, with the most sophisticated architecture and defences, are, by virtue of their proximity to Beijing, the most well-known in popular perception, in contrast to the relatively austere structures across the Ordos or the walls along the strategic Gansu Corridor which were constructed in the 1540s.
Before assessing their effectiveness, it is worth bringing up now a key point of emphasis: the 'Great Wall' was not a contiguous structure, nor was it conceptualised as such, and neither was it considered the sole or even primary defensive installation during its period of use under the Ming. Rather, walls were built in individual, already-existing defensive sectors to supplement their established defensive systems, and happened to mostly link up over time. As such the Ming recognised that the walls were only one part of a more comprehensive system of defences, which had already included systems of freestanding forts, fortified passes, shorter secondary wall segments located well behind the outer wall, and, critically, mobile field armies that could be sent in to break up attempts by nomadic armies to lay siege to these defences, or to cut off their lines of retreat if they did make it through. In fact, the Ming did not refer to a 'Great Wall' at all, nor did they typically to frontier defences in the abstract. Rather, they spoke of the 'Nine Garrisons' (jiu zhen), which clearly (and accurately) pinpoints that the key element was not static buildings, but soldiers. The fortifications were there to assist the armies, not the reverse.
In terms of actually assessing the effectiveness of the Ming's frontier defences, then I would have to say that, well, yes they did work – at least, against the original intended threat of steppe nomads. The force that overthrew the Ming would not come from the steppe, but from Northeast Asia: Jurchen (later Manchu) armies which eagerly (and easily) integrated the expertise of both voluntarily defecting and captured Ming siege engineers and artillerists, and which focussed their efforts mainly in the relatively poorly defended Ming colonial regions out in the Liaodong region, as well as their old allies in Korea, before pushing against the primary Ming defensive network. While Manchu raiding forces would breach the frontier wall occasionally, it would not be until 1644 that the Manchus were able to cross the wall with a full-on army with, critically, a siege train capable of seizing territory long term. They were only able to do so not because of a deliberate and successful breach of the heavily-fortified coastal pass at the Shanhaiguan, but rather because the Ming general commanding the forces garrisoning the frontier, Wu Sangui, defected and allowed the Manchu army through. This defection happened because a rebel army under Li Zicheng, the self-proclaimed Yongchang Emperor of the state of Great Shun, had marched into Beijing and sacked the imperial palace, leading to the suicide of the emperor and the execution of most of the Zhu family. Wu could either throw his lot in with the rebels who had murdered his old emperor, with the squabbling Zhu claimants in south China, or with the ascendant Qing state, and decided to hedge his bets with the invaders.
In that sense, the Ming's defence system was entirely effective. Outside invaders were never in and of themselves able to effect a meaningful breach, and the Ming would in the end not fall to an external invasion, but instead to an internal crisis. Yet Waldron would argue that wall-building was, nevertheless, an admission of failure. Traditionally, Chinese rulers, officials and generals had recognised three broad approaches to frontier management: aggressive military policy to achieve aims by force or the threat thereof, often termed jiao ('extermination'); if that failed, material concessions and carefully manipulated trade policy, typically termed fu ('conciliation'); and if that failed, then defensive military policy, principally through investing in fortifications. Military interventionism was most likely to get you what you wanted, economic manipulation would broadly prevent outside aggression but gave you limited control over the specifics (and might be unpalatable to those convinced of Chinese cultural superiority), and while fortification was cheap by comparison, disengagement let your potential enemies build up their strength, which if it got out of hand could overwhelm any amount of defensive buildup. This is what happened to the outer Ming defences in Liaodong after the Jurchen campaigns began in 1618, and while there was a prolonged standoff at the Shanhaiguan which was in the event broken on the Ming side by the Shun revolt, Manchu expansion into Mongolia meant that their forces were only getting stronger.
So in that sense, it must be acknowledged that the Ming defences were never confronted with being strained to their breaking point. Nevertheless, that still does mean that the Ming defences – excluding the forward defences in Liaodong which fell to the Jurchens and Manchus before 1644 – were effective against the threats they actually faced, which is about as good an assessment as you can give. The issue is that this was a relatively best-case scenario outcome for what was, in the broader sense, a serious case of policy failure.
Eeeeehhhhh...define 'effective'? As EnclavedMicrostate says in their compilation post below, "Well, yes, but actually no, but also yes?" More can always be said on the matter, of course, so further posts will be welcome; however, as "was the Great Wall effective" is one of the more common questions about it, we do have several previous posts on the matter: