The answer would be natural selection.
The female deer might consider the large antlers of the male deer to show of certain genetic qualities that have a higher probability of reproduction, as well as a higher social status among deers.
This means that if she picks him as her mate during this season, their offspring will have a better chance of survival compared to her picking another deer with smaller antlers.
This is called natural selection because she will pick the deer that is most adapted to that environment. Thus their offspring can be ensured to have the highest possible probability to survive.