How would I explain an 'open set' Looking for an intuitive explanation.
An open set is a set where every point has some "wiggle room" without leaving the set.  No matter which point in the set you pick there is a little bit of space around that point (in every direction) that is still in the set.  In other words, no point in the set is on a boundary (if you were on a boundary, you couldn't move at all in the direction that would take you across the boundary).
Intuitively, an open set is the set that does not include both endpoints.

For example, (0,1) is the open set; [0,1] is the close set, and (0,1] is neither open nor close.