What is the reason behind penicillin only killing bacterial cells and not host cells?

Penicillin is a group of anti-microbial drugs/antibiotics that are obtained from different species of Penicillium mold. They are specifically used against bacterial infections.

The specific action of penicillin is to attack the cell wall of bacterial cells. Since human cells do not possess cell walls the penicillin drug does no harm to the human cells.