The RR7 is a low-voltage controlled, latching relay that can control line voltage devices up to 277vac. The small red/blue/black attached leads are:
Red - pulse on
Black - pulse off
Blue - common
The above leads are all low-voltage signals from the transformer and switch.
The relay is normally rated for up to 277vac and 20A, so it can handle a fair load.
When 24vac is momentarily applied to red, the relay closes, and it applies the line voltage to the attached lamp. When 24vac is momentarily applied to the black lead (both of these are the smaller leads attached to the relay), the internal relay contacts open, turning the attached thing off.
The load contacts would have 120vac attached to one side, and the lamp you want to control's black lead would attach to the other contact. The lamp's neutral connection (white) would not be attached to the relay at all, but needs to be attached to the supply's neutral connection.
So, if you attached 120vac to any of the smaller leads attached to the relay, you burned it up and it will need to be replaced.
Think of the relay as a latch - red pushes it closed to turn the load on, black pushes it open. It only takes a short pulse on those leads to open or close the relay. There has to be a low-voltage transformer somewhere to make this all work. that would also need line voltage going into it so you had the 24vac available to control the relay via the low-voltage switch.
This link is where I got that info from...it shows other things, but describes the relay operation... http://www.alarmsystemsdist.com/mc_files/2/ACF2C47.pdf
If none of this makes any sense, you'll probably have to call an electrician.