If it's between the foundation slab and the bottom course of brick, then it's a bond breaker. It allows the brick and foundation concrete to move independent of each other. Since concrete and brick have vastly different coeffecients of thermal expansion, the brick expands a lot more than the concrete and often will break off the corners of the foundation when it gets hot unless a bond break is in place.

The other thing it could be is flashing to divert water. Brick is not a waterproof system. Water will saturate the wall in a rain storm and permeate through the brick into the air cavity (the gap between the house wrap and the back of the brick). Between the the first and second course of brick, they flash the air cavity in order to divert the "mositure" out of the air cavity. In Texas, they simply put weep holes along the bottom course to allow water to escape.

You can trim back the paper. It's not a big deal.