The term CSS delivery simply means "the way CSS stuff happens on a webpage". CSS can be used many ways by a web page and still work. Since there are many ways to use it, there exist many different CSS setups. Your CSS should help your webpage render fast, not slow down your webpage.
The way CSS is used on a webpage has overwhelmingly been determined by designers, not website owners. So the web designer is making lovely, well commented CSS code and has been placing it in several different files for clarity. They think, with merit, "I have done an amazing wonderful job". This is what they have been taught.
Unfortunately this practise and others ends up killing the performance of web pages.
As this realization gets out there, you will notice that web designers will start making code that helps their users by working as fast as possible, however, for the moment... You probably have CSS that is hurting your website rather than helping it.

One of the easiest ways to improve your application’s performance is by putting a caching solution in front of your database. In this tutorial, I’ll show you how to use Memcached with Rails, Django, or Drupal.
 Memcached is an excellent choice for this problem, given its solid history, simple installation, and active community. It is used by companies big and small, and includes giants, such as Facebook, YouTube, and Twitter. The Memcached site, itself, does a good job of describing Memcached as a “Free & open source, high-performance, distributed memory object caching system, generic in nature, but intended for use in speeding up dynamic web applications by alleviating database load.”