Bacteria are prokaryotic and human cells are eukaryotic. So there are basic yet drastic differences in the features of a bacterial cell and a human cell. When a particular antibiotic is designed or say used against a bacteria, it targets a bacterial component or characteristic. Also, the antibiotics are target specific and those compounds won't go hunting down each cell they come across. Since those target components or characteristics are absent in a human cell, they are not going to be acted upon by the antibiotics and they survive.
For example, penicillin is a beta lactam antibiotic and it targets the peptidoglycan cell wall. Due to the breaking of cell wall, followed by leaking of the cell components that particular cell dies. Now penicillin will work only when the target cell has peptidoglycan cell wall, otherwise it won't. So a human cell, which lacks peptidoglycan cell wall will remain unharmed.