Penicillin prevents a bacterium from producing a unique molecule in its cell wall. Why would you expect penicillin to kill bacteria but not human cells?

Simply, because human cells does not contain cell wall, but rather cell membrane which lacks peptidoglycan, and therefore not sensitive to Penicillin.

Penicillin usually targets peptidoglycans especially gram positive bacteria by inhibiting the formation of cross-links and cell wall formation processes for the lay-down of peptidoglycan. Hence the bacterial lose the protective, rigidity and barrier function of peptidoglycan. Consequently, penicillin perforated bacterial cells, fluid enters by osmosis, antibody gain entries to destroy, and the cells loses pressure and burst.

Explanation:

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The fact is Most bacteria produce a cell wall that is composed partly of a macromolecule called peptidoglycan. Human cells do not make or need peptidoglycan. This peptidoglycan is the target for Penicillin. It prevents the final cross-linking step, or transpeptidation, in assembly of this macromolecule. The result is a very fragile cell wall that bursts, killing the bacterium. No harm comes to the human host because penicillin does not inhibit any biochemical process that goes on within us as we don't possess peptidoglycan.