Depending on the age of the house (breaker box), breakers do wear over time
and become more resistive. When you turn your AC on, it gets very hot and
that's what typically causes breakers to trip. The breakers trip when they
get hot due to overcurrent, or just old age.

Check the fan on the AC unit. If it is siezed or shorted that can trip the
breaker. IF it is open and not running that can also trip the breaker by
causing the compressor to draw to much current. After checking this
replace the breaker if you can DIY it.

I have also heard that this can happen if the wire to the breaker is
loosely connected. You may check to see if it is loose and or corroded and
then try to tighten and/or replace it. Please whatever you do, remember to
shut off all the power to the electrical box before you start tinkering
around with the breakers.

Hope this helps.

Mike