Spacetime is like your room. You can move freely in your room in every direction. And as you move the time moves forward. So that is spacetime. You move through the room and while doing that you also move through time.
The continuum part ist mostly Scifi for sounding fancy. But a continuum is sth that smoothly goes along and has no jumps. Look at your linear. It is a continuum of a one dimensional space. Now look at the markings, they are not. They jump from one distance to the other. They are discreet.
Your linear is a continuum of a one dimensional space with discreet markings of a one dimensional space.
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