Wowzers, where to start.
4GS: we classically think of us having 3 dimensions -- up and down, left and right, forwards and back. spacetime continuum states that we can view time as another dimension in our equations (general relativity stuff often). The fact that it's a continuum means that there are no small 'gaps' anywhere. You could move forwards by an inch, or a quarter of an inch, or a millionth of an inch, etc. Or, it can specify properties of the metric that is described on the manifold.
tiggerblue and China Doll: physicians are doctors!!! I think you mean physicist.
Parallel universe: the above describes the many worlds interpretation of quantum mechanics. This is not the only idea of parallel universes.