Many, many specific functions, but they can best be summarized this way:  
the cell membrane forms a barrier between the inside of the cell and the outside,
so that the chemical environments on the two sides can be different.  The cell controls
those differences so as to optimize the workings of the chemical machinery inside the
cytoplasm.  The cell also causes brief changes in the internal environment by moving stuff across the membrane in a controlled way.  These changes are the ways in which
cell respond to events in the outside world .