EDTA is a chelator of metal ions like calcium and magensium. It is used with trypsin because it helps bind up the divalent cations in the medium. It helps to keep the cells from sticking to each other.  If its not there….you would need a higher concentration of trypsin to get the cells to detach.  For the same reason, you should not use a PBS with calcium and magnesium to wash the cells as it may cause the same problem.