The original switch had two black wires going to one terminal, and one black wire attached to the other. Here's why:
Of the two blacks, one was the HOT wire from the panel. The other is a jumper to the next bedroom (the other bedroom recieves its power through that wire) The two wires were connected BEFORE the light switch (incorrectly, but I'll get to that later) so that the second bedroom has power available to it no matter what you do to the switch.
The single black wire feeds power to the light in your room, but only when the switch is turned on.
You should have 3 white wires all wire-nutted together in the same box, but tucked all the way in the back. If not, they exist elsewhere, although I cannot for the life of me understand why.
The reason the power came on in the other bedroom with your meter attached is that the meter was bridging the gap between the HOT wire and the jumper wire to the bedroom. I don't recommend doing this with your amp meter if you want to keep it for very long. The circuitry in the meter is not designed to handle loads like that and I'm surprised you didn't damage the meter in the process.
To wire your switch box properly, (as far as my non-electrician mind knows) you should have the HOT and jumper wires wire-nutted together with an 8" lead (an additional 8" long piece of black wire) The lead goes to the hot side of the switch in bedroom 1. The single black wire still connects to the other side of the switch.
All three wires have to be connected somehow to the switch. Don't ever connect more than 1 lead to a screw terminal.