Sometimes a song does not begin on the first beat of a bar. Any notes which come before the first full bar are called lead-in notes (or pick-up notes). When lead-in notes are used, the last bar is also incomplete. The notes in the lead-in and the notes in the last bar add up to one full bar. Here are some examples. Notice the Bb note written as a key signature in these examples, reminding you to play all B notes as Bb.
This early Jazz standard was a favorite with brass bands in New Orleans. It contains three lead-in notes.
This symbol is called common time. It means exactly the same as *.
In this example there is only one lead-in note. Notice the use of slurs here also.