Sticking points in the pedal stroke
Either the rear wheel or the crank bearings are binding at some point in their revolution, or (or possibly there's something going on with the chain). The first thing to do is track down where the problem is.
Check first for obvious stuff, like is the rear wheel out of true and rubbing the brake blocks?
The next easiest thing to do first is take the rear wheel out, remove the quick release skewer and check the bearings. Turn the axle with you fingers, does the axle have a tight spot, do you feel excessive resistance or 'notchiness'? Push and pull the axle about to check for play, if you can feel the axle moving more than a tiny bit there is excessive play.
If the wheel bearings are is OK, check the crank. Most front derailleur cages have a small screw that allow them to be opened and the chain removed. Get the chain out of the cage and off the chainrings (it's awkward but possible). Spin the cranks by hand, again checking for a tight spot, excessive resistance, 'notchiness' and play.
The wheel is the problem fixing it depends on the type of bearings. Some hubs have 'serviceable' bearings that can be disassembled, some have pressed in cartridge bearings. If the crank is the issue, a new bottom bracket is required.