Breeze
Jack the car up, take the drum off and take a look. You don't have to disassemble the whole brake. Just take the Drum cover off, and take a look. It's probably something simple like the thin metal behind the brake is bent or something may be hitting the tire. Just look at it. You'll probably notice what it is right away.

odomatt
might be a out of round drum

baldie
sounds like you have a spring off the shoes or it,s broke.

Technobuff
I reckon you have an eccentric or out of round drum. Or perhaps a cracked one, or one where the centre and the actual drum have separated a bit. How long since the brakes were looked at? Is the wheel tight? In an eccentric brake drum, the shoes have to slide about to follow the eccentricity. Eventually this will cause excessive wear on the side of the shoes, and grooving in the brake backplates. So often a click is what occurs as the shoes try to compensate. Check everything out. The drum for cracking, look at it, suspend it on 1 finger and tap the outside sharply. It should produce a ringing sound if OK, but a dull "thunk" if it is cracked (or separating from its centre, if it is a 2- part drum). Also look to see if the drum internal surface is in good condition or not. Worn steps generally means re- machining the drum, but check the maximum diameter is not (or might already have been), exceeded.