The idiom is not "get home". it is "to get something home". More commonly this is expressed as "to drive something home".
drive your message/point home
to state something in a very forceful and effective way:
The speaker really drove his message home, repeating his main point several times.
Cambridge Dictionary Online
The original expression was "to drive a point home". This metaphor refers to driving a nail into a piece of wood or a peg into a hole. It connects with the idea of making a point in an argument. Note that 'home' means 'rightful place'.
The expression "to get a message home" is two steps away from the original idea.
This answer was posted simultaneously with others. I see that there is some overlap.