To understand how penicillin fights bacteria, we first have to understand a little about them. Bacteria are microscopic one celled organisms. The are all around us, but most of them are harmless. Bacteria are different than animal cells in that they have ta cell wall sandwiched between two cell membranes, whereas an animal cell only has a cell membrane. This cell wall is very important for the bacteria because it allows them to survive under conditions they wouldn't be able to handle without it.
Bacteria lead a simple life.
They basically spend their time absorbing nutrients from their surroundings and growing until they are large enough to split in half. This is how bacteria reproduce. As they grow they have to make more cell wall just like everything else in the cell. Penicillin works from inside the bacteria by preventing the bacteria from making more cell wall. The bacteria will grow, however, and eventually burst through their cell wall.