Well this is all on theory, since we've never even seen a black hole, just things we think are black holes through telescopes and other instruments.
First, what is time?
Black Holes don't distort "time", they distort "gravity".
Everything is affected by gravity. Every reaction. Every movement of energy.
If everything past the event horizon of a black hole is under more gravity, then everything happens slower.
This means that "time" is slower for that space, because reactions and all the things we use to measure "time" are slower. Objectively, "time" as a concept marches on, unaffected by gravity, but because we cannot measure time except by how things *happen*, it's impossible to tell. For all purposes, the greater the force of gravity in an area, the slower time runs.
In most instances, this isn't noticeable.
For a good example, there are satellites in orbit going so fast (6000 mph), they have increased mass due to their rate of speed, and age at around 7 microseconds less than a stationary object in no gravity per day. Some of these are GPS satellites, and they take this into account when calculating things.
Another great example are CRTs. The electrons fired by the electron gun are going about 30% of the speed of light. They had to account for time dilation on those electrons when designing the magnets for them.