Xbox Live allows you to play games against other people online as well as download demos, trailers, and even full games in the Xbox Live Arcade. You get to choose a nickname (called a Gamertag) which is how you will be known to other people in any games you play. You can keep friends lists in order to keep in touch with real life friends or new people you meet online you like to play with.
To use Xbox Live you have to have an Xbox or Xbox 360 as well as a broadband internet service provider. Xbox Live is a subscription-based service that can be purchased in 1 month, 3 month, and 1 year periods. You can either buy subscription cards at retail stores or you can use your credit card on the Xbox or Xbox 360 itself to sign up for Xbox Live.
New to Xbox Live on the Xbox 360 is that there are two levels of service. The Silver level is free and lets you download things from the Xbox Live Marketplace, chat with friends, and share your gamer profile with other users. You can't play games online, however. The Gold Level is a paid service and gives you all of the Silver level benefits along with the ability to play games online.