Mowing has two primary advantages. First, it reduces weeds and second, it improves the pasture productivity.
Mowing before the weed seedheads are produced, prevents weeds from spreading. Mowing also keeps the plants shorter, which dairy animals prefer because it has less fiber, is higher in protein and more nutrients reside in the younger leaves and stems.
The other benefit to for mowing your plot allows plants to tiller (branch out) new shoots which is where the highest protein levels occur.