Battery died, weird noise from dash

My battery died the other night, and I thought that was it, because I had it tested and they said its wouldn't take a charge. Today I thought it happened to my new battery, but I wiggled the terminal, and it started after that. When I got home, I was testing to see if my alternator worked, so I left the lights on with the engine off. I walked off, came back and I hear a clicking noise comming from the round relay on the fusebox. I disconnect it, plug it back in, and the noise goes away, and the lights come back on..What the Heck? I wouldn't blame you if you didn't understand any of this, cause I don't quite understand it myslef. A couple of days before the battery died, the radio would click on and off whenever you turned the truck off, and left the accesories on, I just don't understand why the radio wouldn't have enough power, if the battery was dying, because it still started. I'm worried that I screwed something up with all the wiring I've been doing.