Twitter is a company that asks - What are you doing? - and they share your answers with anyone else who wants to know. You can answer the question anytime you want, as often as you want.
You answer the question through your cellphone, the Twitter website, or chat. People who want to get your answers receive them also by cellphone, website, or chat.
If you find someone interesting in Twitter, you can also 'follow' them to get their answers.
Each answer can be at most 140 characters long.
Twitter doesn't care what kind of cellphone you have, so it doesn't matter whether or not you use an iPhone. However, iPhone users can use a website called PocketTweets to make using Twitter on an iPhone easier.