Take a look at some answers to frequently asked questions about The Open:
What's all this "The Open" stuff? I thought it was the British Open.
What you call it has historically depended on where you were. If you were in the U.S., you called it the British Open, just as Europeans refer to the PGA Championship as the U.S. PGA. Outside the U.S. it generally has been referred to as The Open Championship. The preferred name of the organizers is The Open.
How old is it?
It's the oldest golf championship, dating back to 1860.