A measure in music is the space between two vertical bar lines on a staff. A measure of music is comprised of beats and rhythms according to the time signature at the beginning of the staff.
Time signatures indicate the type and quantity of notes that are in each measure. The top number is the number of notes per measure, and the bottom is the type of note. For example, if the time signature at the beginning of a piece is 4/4 time, represented by a four over another four, there are four quarter notes in that measure. A quarter note is accepted as the standard "one beat" note in music.