advantage of apc module

The APC PHP extension consists of two parts:

1. The opcode cache
2. The data cache

The first one caches your semi compiled .php files in the memory, so the server doesn't have to compile all the php files on every request.
The second one is a not persistent shared data storage. This module allows you to use the second one as Drupal cache backend.
An anonymous visitor visits your homepage. You store the output to the APC data cache. An other visitor comes, it can find the cache entry of the page in the APC saved previously.
In Drupal there are several types of cache which can be stored in APC, not just the page cache. You can find the temporal information about the views, forms, fields, the bootstrap etc in the Drupal cache.
Drupal by default uses the database to store all these records, but MySQL adds a complexity (like durability) which is not essential to maintain the cache and a key-value store (like APC or MemCache) may match your needs better.

You can find more information browsing around to figure out where to store which Drupal cache bins. For active help you can join #drupal-support channel on freenode.net.

I was wondering the same thing. I have a multisite setup, and apc running at the server level. I haven't seen too many discussions about if this module would still help.

A PHP cache system, like APC would help any site that uses PHP to generate pages.

This applies regardless of the CMS base or type.

In addition, Drupal is able to use such a cache for data store as well (as stated previously @ #1).
Primarily, the best performance comes from simply using the PHP opcode aspect of APC.

This is true for multi-site as well, just be sure there is enough APC cache size given as to avoid cache fragmentation. Otherwise, the benefit of such a cache is lost.

Please see #1870832: What does this module provide versus just setting up APC for information.