@Dolph, in the simplest term, think of Spring as your application framework at the highest degree. This "framework" provides several "component buckets" where you can easily plug in different types of implementations. For example, for ORM, you may choose to use Hibernate over JPA or TopLink, for front end, you may choose Wicket over Struts or SpringMVC, and so forth.
The whole beauty of this (besides all the goodies stated in other posts) is it allows you easily swap out any of these implementations easily in the future. So, you can essentially rip out Hibernate one day and replace with TopLink, and it will never cause ripple effect to other components.
Another beauty of using Spring is your code becomes less clutter and has loose dependencies with other classes because you spend less time creating new objects yourself, Spring handles that for you. That said, you will quickly realize how easy for you to test your code because your API to be tested becomes very atomic. This is one primary reason why folks get discouraged in writing testcases, because they quickly realize that in order for them to test one API, they have to construct whole lot of things just to test that. Because of that, the whole process is brittle, imagine if you change that API, you need to reconstruct everything before testing it again.
Pro Spring book is good, mentioned by @JLBarros. I like Spring in Action very much. It is very very easy to read when I first got started with Spring. This is probably one reference book that I read from skin to skin.
I like the In Action series, but I wasn't confident in the book after reading the Table of Contents... but then again, I had no idea what I wanted out of Spring, so I didn't know what to look for! The second edition is expected to come out Dec 2010 as well.
The In Action by no means have all the details about Spring. For that you need to refer the springsource website directly because they have the most complete documentation I have ever seen. The In Action helps me to get started right away and the explanations are very easy to understand. When I need more info after that, I will dig around springsource.