Xbox Live Silver - this is the free level of LIVE that anybody with an Internet connected 360 can sign up for. This level gives you access to almost all of LIVE's features except for online multiplayer, and occassionally delayed access to new demos.
Xbox Live Gold - the only paid membership level in LIVE. This gives you access to all features of LIVE including the online multiplayer and earlier access to some new demos. There are a variety of payment schemes available to provide more flexibility in how long you want to subscribe for the service. However, the full year membership is by far the best value/month which can be frustrating for people that don't use their membership all the time.
Gamertag - No matter which level of service you subscribe to, you'll have a unique gamertag identity that stays with you across games, and even across consoles. All information is associated with your gamertag, including your reputation and skill rankings. If you switch between Gold and Silver membership levels you maintain the same gamertag. You can change what your gamertag is (but not the information associated with it) by paying Microsoft $10.
A significant portion of Xbox LIVE's revenue comes from it's digital distribution services known as Xbox LIVE Marketplace. Unfortunately, Microsoft has opted to use their own proprietary system called "Microsoft Points" which obfuscate the true dollar value of the items sold.
Themes and gamer pictures - Xbox 360 dashboard themes can be purchased from the marketplace to bling out your console.
Xbox LIVE Arcade - these are smaller games that range in price from $5-$15 and offer upgraded retro titles or brand new titles that are smaller in scope that traditional retail discs. Every XBLA game has a demo so you can try before you buy. Many people compare the service to the shareware days of the late 1990s.
Xbox Originals - original Xbox games that can be purchased and played on your Xbox 360. No upgrades/improvements have been made to these games.
XNA Community Games - a service introduced in fall 2008, the community games lets anybody make a game and sell it to the Xbox Live audience. This is Microsoft's way of opening up the platform and giving independent developers a better chance to get noticed and make money.
Video Marketplace - an area to download movies and television shows. The selection in the United States rivals that of many top tier video distribution services, however the selection in other countries is vastly inferior. Many titles have both standard definition and High-Definition feeds available.