Twitter can be accesed from some mobile phones and from the Internet. Think of it as the facebook status bar, except that it has a 140 character limit.
Personally, I like it. It's nice to see what my family and friends overseas are up to.
Bluetooth is a protocol for connecting two mobile devices via radio waves. Essentially, it allows you to pull information from other Bluetooth-enabled phones in the area, such as their number, and it allows you to send data, such as images, videos, text, etc.
If your cell has bluetooth, try activating it in a shopping and you'll see a bunch of numbers.