The Space-time continuum is a scheme developed by Hermann Minkowski, who was Albert Einstein's former teacher in mathematics. According to this scheme, 3 dimensional space and 1 dimensional Time are basically the same. The Space and Time are intertwined in such a way that they form a 4 Dimensional continuum which is also known as Minkowski Space.
In Classical Mechanics, time is considered constant or universal and hence Euclidean Space or 3 dimensional space is used but when a body moves at speeds close to speed of light, time is no longer constant rather it becomes relative. That is, close to speed of light, time slows down.
In General Theory of Relativity, Albert Einstein proposed that the curvature of Space-time continuum due to a certain mass or a body is actually the Gravity.
