What does "24 on center" mean
"On-Center" is a term to indicate measuring from the center of one to the center of the next.  This has the advantage of not getting into the detail of the actual width of the material being used.  If you try to space a set of 2x4's by measuring between the side of one, to the side of the next, then you have to take into account the actual width of the stud. (24" - width)
A "2x4" is a nominal size, the actual size is less, and that's just a detail in the bigger scheme of things.  If you do "On-center" measurement that issue is brushed away.