What exactly is an advanced object cache?

I’m reading this article about fragment caching. It seems self explanatory except for this line:

based on the assumption that you have an advanced object cache available.

What exactly is an advanced object cache, and how can I check for one/implement if not already available?

An advanced object cache is a cache mechanism that can store data that persists beyond a single request. A couple of popular object caches for WordPress are APC and Memcached. The WP_Object_Cache class Codex page has a list of links with more info on advanced cache options.