To show what's on your computer screen on a projector, you must go to the Displays pane in System Preferences.
Go the Arrangement tab and choose the "Mirror Displays" checkbox.
Otherwise if left unchecked, your computer will display an extended desktop. You'll notice when it's unchecked that you can move the cursor and windows to this extended desktop. An extended desktop is more useful when you've got an extra monitor that you want to attach to your computer.