This post is getting fairly old, but I’m going to assume that you’d still like an answer.

The Paris Commune was described by Marx himself as a Sphinx (Karl Marx and Friedrich Engels, On the Paris Commune, Moscow, 1971, p.68) because the precise aims of the communards and the meaning of the Commune itself were mysterious. In this sense, it’s hard to gauge if it achieved any of its aims, since the closest thing to a statement of goals was probably the April 19 manifesto which most groups expressed dissatisfaction with due to it representing a lowest common denominator of the various groups’ goals (Donny Gluckstein, The Paris Commune, Chicago, 2011, p.167). Nevertheless, the implementation of several key measures marks the Commune as a significant event for Marx, Engels and anyone who followed in their tradition.

1) It represented a challenge to the existing order

The Commune was an explicit rebellion against the French government and its armed forces, even seizing their weapons and property. This alone is fairly significant throughout world history, though admittedly there is little in this to separate the Commune from any other mass revolution. That is, until the following is also considered.

2) It presented an ideological challenge to governments of Europe

This is perhaps the most significant aspect for the Commune’s many socialist admirers. Representatives within the commune were elected but remained instantly recallable. Essentially, this was intended to ensure that elected representatives could not make false promises or have a change of heart, straying from the desires of their electorate. The idea was to have an ongoing, dynamic democracy with high accountability. This was reinforced by the fact that elected representatives did not receive monetary privilege, receiving only a working person’s wage (there has been some debate about this, though the evidence seems to suggest they received, at most, a skilled worker’s wage (A Arnould, Histoire Populaire et Parlementaire de la Commune de Paris, Lyon, 1981, p. 168)). For these reasons Marx dubbed it “the glorious harbinger of a new society.” (Marx and Engels, as above, p. 97)

3) It demonstrated the germ of different forms of economic organisation

This point is perhaps more difficult to see within the Commune since it existed so briefly. Nevertheless, the unique political situation within Paris also gave way to the beginnings of new ways to organise the economy. Most of these were based around worker cooperatives which there are no direct analogues of in the modern mass-production economy. Roughly, they were small associations of handicrafts workers which often collaborated and sold their goods through a mass employer. As an example of the new twist the Commune put on these organisations, take the situation surrounding military supplies. Some workers discovered that because the Commune was ordering military supplies at the lowest possible price, French employers were reducing their workers’ wages by up to one third. After intensive debate involving a wide array of parties, including garment workers, the decision was made to form new contracts guaranteeing higher wages for the military supplies workers, even though this jeopardised the security of the Commune. The argument made was that the ideal of the Commune in the minds of workers was as essential to its survival as military armament. Additionally, they tried, wherever possible, to bypass employers and negotiate directly with worker bodies (G Bourgin and G Henriot, Proces-Verbaux de la Commune de 1871, Patris, 1924, p.351-352.)

4) It provided essential lessons for the First (and later) Internationals

The Communist Internationals drew lessons from the Commune which their leaders deemed to be vital. In particular, the role of organisation and spontaneity in revolutions (an ongoing debate), the extent to which anarchists, socialists, utopian socialists, Blanquists, etc. could cooperatively organise, etc. These points go towards the second part of your question as to why the Paris Commune ultimately failed. Given the rules of this subreddit, I doubt a satisfactory answer can be provided since explanations very quickly become political. However, I will try to summarise the main points of view. First, Marxists tend to point to the lack of an organised political party with clear ideas to cohere around, in the vein of the Bolsheviks. This led to a series of poor tactical decisions such as reluctance to march of Versailles when they had the opportunity. Particularly harsh critics dismiss the entire Commune as drunken debauchery brought on by starvation and excess wine (E A Vizetelly makes this claim in My Days of Adventure, or the Fall of Franc, 1870-71 but provides no evidence). Finally, more moderate types tend to make the same arguments against the Commune as against Communism more generally (it violates greedy human nature, the required level of planning is impossible, if everyone is equal then there’s no incentive to work hard, etc.)

In short, while the Paris Commune was brief and fleeting, and did not have many permanent effects on the French political system, the ideological challenge that it presented is why it VERY quickly became a “legend” among socialists thereafter.