4 black wires for light switch box, 3 white w/ Picture
If your new switch is the same as the old you have skinned a wire or have hot touching ground.  You should be able to connect all of the black wires together and the light would be on all the time and not trip the breaker . The switch is a simple open closed device. 1 hot feeding another device and the switch to the light when the switch is in the on position all the wires are connected. You need to find the short, it could be by chance the lamp failed with a short , not likely but a possibility a skinned black wire touching the metal box will cause the breaker to trip. 

Another possibility is a switch leg where white is used as a hot I cannot clearly see the rest of the wiring , if you only messed with the 1 pig tail (just black wires) look for the damaged insulation.