At the heart of many modern PHP application there is an IoC Container, short for inversion of control container. When people talk about a "dependency injection container" or a "service container" they mean the same thing. It's purpose is to manage class dependencies. Though the concept is relatively simple, it can come across very confusing if you've never worked with one.
In a new post on his blog Matt Allan builds a simple one from scratch. Check it out if you're struggling with understanding how the IoC container works.
If you are writing modern PHP, you will run across dependency injection a lot. Basically all dependency injection means is that if an object needs something, you pass it in. ... Dependency injection makes your code more flexible and easier to test.
EDIT: mattalan.org seems to be down, but you can still view the post in Google's cache.