This is a long article that is one of the seminal works of theory in the field of International Relations. A full summary is impossible in the space available here. What I can give is a very basic summary of Wendt's major point.
In this article, Wendt is taking issue with the main claim that realists make -- that states are forced to act in certain ways because the international system is anarchical. Realists claim that anarchy, by necessity, causes states to come into conflict with one another.
Wendt takes issue with this. He argues that there is nothing in anarchy that makes conflict necessary. Instead, he says, states' actions towards one another are based on their attitudes towards themselves and toward other states. In other words, Wendt is saying that a state develops its own identity and it gives identities to other states. It acts towards other states based on how those identities match up.
Perhaps you can think of this by means of an example. Iran sees itself today as a major Islamic power that should have more influence in its region. It sees the US as the major threat to it both as a Muslim country and a regional power. Therefore, it acts aggressively towards the US. By contrast, Saudi Arabia does not act aggressively toward the US because it has not constructed this image of the US as a "Great Satan" that hates all Muslims.
So what Wendt is saying is that states construct visions of themselves and others and act based on those visions, not on the basis of the fact that the international system is anarchical.