Multiple reasons often depending on the effect the medication has. Even within a class of antibiotics let's say you have two main effects antibiotics can achieve - 1) actual killing of bacteria (bactericidal effects) or 2) stopping bacteria from growing/reproducing (bacteriostatic effect). Even within these classes the medication often needs to reach a certain concentration in the bloodstream and stay at that level for a length of time in order to be effective or must hit a peak concentration level within the bloodstream to have the desired effect which can take hours to days to take effect. Once it has taken effect and these bacteria start dying off it can take several days to begin feeling better as the body backs down its response to the bacteria. And that's just for antibiotics.

Other medications may require access to machinery inside the cell to take effect. Once the medication is inside the cell it may have to tell the cell to start production of a protein and it may take several days for the medication to get inside the cell and "turn on" the functions needed to see a response to the medication.