I have several MR16 2 pin style light bulbs in my kitchen - The other day the trip switch for the light bulbs tripped when turning these bulbs on - I went and flipped the trip switch and tried again to the same result. This happened three times, the same number of times as the number of MR16 lights. Now the trip switch doesn't trip but also none of these bulbs turn on, and replacing the bulbs with new ones doesn't work. I don't know much (anything) about lighting, these bulbs were in my house when I moved in, and was wondering if anyone could help me work out why this is happening and what I can do to fix it.
You're using MR16 50W 12V Halogen Flood Reflector Light Bulbs is my guess. Some of these light fixture for these light bulbs have a small transformer (4 wires - 2 pri (blk & wht color) & 2 sec -- about 1 inch x 1-1/2 inch x 1/2 inch) for each light bulb. They cost as much as a light bulb (maybe more), My guess is this one was on its way out and is now open circuit.
Somewhere in your light circuit there was a short circuit that caused the breaker to trip. By repeatedly trying to reset the breaker, the point at which the fault occurred finally blew itself apart. Now instead of having a short circuit you have an open circuit. Proper troubleshooting will allow you to find the problem's location, but explaining this procedure is somewhat challenging in this forum.
You killed your breaker. And there was a fault that needed rectifying. It could have been one lamp that developed a short- which has since been replaced. Or a wiring short- which may still be there.
If you have a multimeter AND your old lamps see if any show a very low resistance compared with the rest of them.
If so your wiring will be OK, and all the same resistance lamps will be OK to use. If they all show the same resistance the wiring needs help.