What's a loop current?
The idea of a loop current is that for each loop you can identify in the mesh, you can find one value of current "attributable" just to that loop, and which passes through every leg of that loop. 

Any leg (edge) of the mesh may be involved in more than one loop, in which case the actual current in that leg is the sum of the loop currents of those multiple loops.

It's like the flip side of the more intuitive observation that currents flowing into and out of a single node add to zero. (All current flowing in must flow out -- current can't just appear or disappear.)