I have the following music notation and I would like to know what does (A) and (A') mean.
It's the form of the piece. As you can see both sections with the A above them have very similar rhythmic patterns and the sections that have A' have different rhythmic patterns then that of A. So the piece has a form of
Another use (not applicable to your example), very frequently encountered in orchestral or ensemble scores is as rehearsal mark. It may be letters or numbers either in a circle or square. They can be recognized as such, since they appear in strict sequence (A, B, C...). Sometimes "I" is omitted not to be mixed up with "J". Their purpose is, to have reference positions in the piece e.g. "lets start at 4 bars after (B)" in addition or more likely in absence of printed bar numbers.