A bit of searching and reading would get you your answers but since you asked: they greatly reduce wobble, let you get some weight off the seat, tuck you in a more aerodynamic position, give you somewhere to have your brake handle, can help steer and generally make you more stable at speed.
I like my handles lower and further out than most.
Here are some threads you could check out
T7 handle…Cambridge style (with drops / fangs)
Handlebar discussion - How to?
Have fun
ERIC