a space time singularity is a point in space-time where an infinity occurs (that is to say there is a discontinuity in the mathematical function that describes space-time). In the case of black holes, the infinity arises in a finite amount of mass \((M)\) being squeezed into a volume \((V)\) of zero size, meaning that the density of the object become infinite. Recall that density is given my \[D=\frac{M}{V}\] and hence, you will be dividing by zero on the bottom line. If you plotted density as a function of volume for a given mass, you would find that at V=0, a mathematical singularity is found.
Since density governs the degree of space time warpage, an infinite amount of mass will warp space time by an infinite amount, meaning that a space-time singularity is formed.