First and foremost, the page history tells you something about who has worked on the page, and allows you to examine the successive versions of the article and the differences between them. Usually by looking through the edit history, you can quickly tell who has made substantive contributions to the article.
If an edit was made by a registered user, you can follow up to their [[Wikipedia:User page|user page]] to see who they are (or at least who they claim to be.). Associated with each user page is an accompanying user talk page, which often gives the flavor of their interactions with other users: is it full of thank you notes or vitriolic arguments? There is also their [[m:Help:User contributions|user contributions]] page, which lets you look at all the work this particular person has done in Wikipedia, including their side of online discussions with other users.
If the edit was made by a user who was not logged in, you can at least get a look at the other contributions made using the same [[IP address]], which are often, but not always, made by the same user. (Many Internet service providers isbrasueissue temporary IP addresses to their users from a pool of addresses: when the user disconnects, the address is returned to the pool for allocation to someone else.) Also, it might be a fixed IP address for a computer in a public place such as a library or school; computers in such public settings can show an extreme combination of excellent edits and vandalism, but you still might be able to see that the particular edit came in the midst of a series of edits that help you gauge the character of who was at that machine at that time.
