I think the word he was looking for was infinite density.
The first idea of a black hole was stumbled upon by someone wondering what would happen if you had a star the size of the sun, but 500 time its mass. Its density would then be so great as to be greater then the speed of light.
That was using Newton's laws of gravity.
Now that we have relativity, we actually do not even need an object to have such massive mass, just the correct density, as when it reaches a certain threshold, the gravity of the object bends all of spacetime in such a way to lead every patch out of the black hole toward itself.
So simply speaking, the Earth is too small to collapse into a black hole, however if by some divine intervention you were to collapse all its mass it would form a black hole with an event horizon on the order of 9millimiter. (roughly 2/5 of an inch).
Naturally, it is currently believe to be possible to have a black hole under only 3 conditions.
1- 3-100 sun masses, we're talking a pretty big star that goes super nova, and then collapse further then a neutron star to form a black hole. In this category, another event might create a black hole in those mass range, such as the merging of two neutron star.
2- supermassive black hole, currently known to be in the center of galaxy, we're talking several thousand to several billion solar masses. Also hypothesise to be the power behind quasars, and various active galaxy.
3- micro black hole, below 1.44 solar mass, and way smaller. Those black hole are currently undiscovered mostly because of their small size, and their origin, as they could only have formed during the big bang. They would atm if current theory hold, be emiting massive amount of radiation. (read a brief history of time for more details or wikipedia is a great help).
Lastly, a black hole is in theory a singular point with zero for all three normal dimension, thus when you try and divide its mass by its volume, you get a very bothersome result, as math currently can not deal very elegantly with division by zero.