Plug ins are “extras,” ways of extending the way wordpress works. Because WP is open liscensed software, anyone can develop extra functionality for it. Some plugins are just for fun — for example, I use one that creates random taglines for my site. Others are pretty important, such as akismet, which helps protect your site from spam.
The plugin above is one of those I don’t think is very neccesary, so don’t worry about it. All it does is make it so you can search these forums directly from the admin page of your blog. If you don’t mind actually coming to this site each time you have a question then it doesn’t need to be installed.
If you downloaded the latest version of WP you should already have a few plugins — Akismet, database backup and I think Hello Dolly.
There are thousands of articles on the codex and most of your questions, such as “What is a Plugin?” can be answered there.