It means which edge of the board you are edging into the water with.
If you are leaning back and cutting through the water on your back edge, i.e. the one behind your heels, that is heelside. If you are leaning generally forward and cutting through the water with the front edge, i.e. the edge in front of your toes, that is toeside.
Heelside is sometimes called backside.
Toeside is sometimes called frontside.
Heelside and toeside can each be either "normal" or "fakie" which refers to which foot you have forward.
Your normal foot forward is the one you feel most comfortable with.
Fakie would then be the opposite foot forward.
Riding "fakie" is also refered to as riding "switch".
So you basically have 4 modes of riding:
Fakie heelside, and
Yeah, it's confusing at first.