Andrew Hamilton’s (has a fantastic website on black holes http://jila.colorado.edu/~ajsh/insidebh/index.html ) definition of a black hole: “Black hole is a place where space is falling faster than light.”
Shown in the figure is the space around a Schwarzschild black hole falling into the center.
Outside the horizon : Space is falling into the BH at a velocity lower than the speed of light. Photons are losing their energy and they get redshifted.
At the horizon: Space is falling into the BH at the speed of light.
Inside the horizon: Space is falling into the BH with the speed greater than the speed of light, carrying everything with it. (Nothing in the universe can move faster than the speed of light, but the universe itself can move at whatever speed it wants to. You have actually already seen an example where the universe expanded faster than the speed of light when studying the Big Bang – period of inflation). Space is falling faster than speed of light inside the horizon, but this velocity is with respect to the observer at infinity. Particles actually move slower than speed of light with respect to space.