AAM provides a way to access same SharePoint content from different URLs. It can be useful if external users in an organization will access the SharePoint sites using a different URL than the internal users.
Here is great explanation from Microsoft Enterprise Search Blog.
Allows you to modify results URLs based on the access URLs for a site. So, for the same result page, a user accessing from an internal URL will see results with URLs matching the internal site, and a user accessing from an external URL may get the same result set but with URLs matching the external site. For example, for the same set of SharePoint content, internal users use http://server to access the site, all the URLs they get in search results are prefixed with http://server/… ; external users use http://www.microsoft.com, all the search results they see are prefixed withhttp://www.microsoft.com.
· Does not require a crawl for the settings to take effect.
· Generates results URLs based on how the site is accessed.
· Is set per farm, so if you have more than 1 search service application in your farm, all of them will use the AAM setting.
Here is a great video session that describes AAM.
Also you can find an extension explanation of AAM and how to configure them from this TechNet page.