The supply line is coming from the right (bottom in your photo) it has a ground, black and white lead, which suggests it's 120V, so the black is live and the white is neutral. It might be a 240v supply, although by current code that should be a 4 wire cable, white (neutral) black (live) red (live) and ground.
The white supply goes to L1 which is connected by a solid metal strip to T1 and the black load wires. I'm assuming one to the compressor, one to the fan, I can't tell which is which - but it maybe one goes to the starting capacitor, which is the aluminum can.
The black supply goes to L2 which is connected by the contactor to T2 and the red load wires
The buzzing could be the contactor, but it could also be the compressor or fan. What Liv is suggesting is that you remove the contactor cover (secured with the Torx screw) and push down on the contactor with an insulated screwdriver. If your contactor is making poor or intermittent contact, pushing down can temorarily fix it. This is moderately dangerous since you're poking conductive metal screwdrivers in live circuits. If the cat decides to join in, or the neighbour's kids throw a ball at you, you may generate a lot of sparks.
Here's what I would do.
With the power off unplug both red wires from the T2, which disconnects the fan and compressor. Use insulated tools, because although the power is off the capacitor can store a charge for some time. Switch the power on. If the buzzing continues it's the contactor.
If not, the problem is with the fan or compressor, this is not a cheap fix and maybe new AC time.