Each Bitcoin is basically a computer file that is stored in a 'digital wallet' app on a smartphone or computer. People can send Bitcoins (or part of one) to your digital wallet, and you can send Bitcoins to other people. Every single transaction is recorded in a public list called the blockchain. Please visit the website below to get more information regarding what bitcoin is and its use case.
Head over to Bitcoin.org's "Some things you need to know" to learn more about Bitcoin!
99Bitcoins also has a very informative week-long "crash course" for Beginners—1 email per day, for 7 days, will get you up to speed on what Bitcoin is.