When you buy a powerline networking set, it comes with 2 adapters. One of them you connect by ethernet wire to your router. Then you plug it into the power socket on the wall. The network data is then sent over the power wires in your house/apartment (by some analog signal that I don't really understand either).
In your room, you'd plug in the other adapter to the wall socket, which will monitor the signal over the power lines and convert it back to the network data. You'd then connect your laptop to the second adapter using a ethernet wire.
It's basically like running an ethernet wire all the way from the first floor to your room, except instead of using ethernet, it uses your power lines.
If you're looking to keep your computer on wireless, you should get a repeater though
As for which you should get, read the reviews!