How frequently are the lights dimming? Every few minutes? Once a second? How long do they stay dim? Do any other lights in the house dim at the same time?

You will want to find out what is on that circuit: Turn on all the lights in the house, and flip your breaker off, and record which lights go out.

Take a radio or some other portable electrical device, and go around the house checking the outlets, there may be some outlets tied into the circuit, although this is rare in newer homes.

Just a start. My floor lamp in my bedroom pulse dims a little when my laser printer is working, because they are on the same circuit, and the fuser in the printer causes it.