Excellent question! Time dilation is a real phenomenon that occurs between observers that are travelling at different speeds relative to one another. It is a result of the unchanging observable speed of light, regardless of your position in space, and is the basis for the theory of special relativity. If you are interested in the details (which often become mathematical), I recommend this online lecture series:

In short, any observable event will appear longer to an observer outside the reference (moving toward or away) frame of the event than it does for an observer in the same reference frame. And both observers are simultaneously correct – this phenomenon is not due to information propagating through space or some property of the observed event. An apt example is called the “Twin Paradox”: if a twin spends a significant amount of time travelling at great speed (close to the speed of light), they will experience less time than their twin who stayed at home. Although they start life being the same age, the travelling twin will experience less time for every year of the stationary twin’s life. This is explained in-depth here:

This occurs any time when two observers are moving with respect to each other, such as in a train or airplane, but we rarely travel at speeds where the difference can be noticed. As such, the effects of extreme time dilation can seem very strange, making it perfect to feature in science fiction like in “Interstellar”.

So, in “Interstellar”, the crew is already dealing with some degree of time dilation with respect to Earth because they are travelling quickly away from it toward and through the “wormhole”. However, one of the planets that they are investigating (on the other side of the wormhole) is located “closer to” a black hole than they thought. Black holes are much more massive than our sun so it’s gravity field is stronger. In order for a planet to be orbiting it, it must be orbiting very fast. In order to land, they will have to spend a significant amount of time (from their perspective) at that fast speed to match the orbital speed of the planet. Because the events on the planet are in their reference frame, all outside observers will perceive them as taking longer than they experienced them, and the faster they travel, the slower their actions will appear from Earth.

I have not seen the movie, but yes,it is true. This is because of the way that general relativity works, not special relativity.

This does matter even here on Earth, actually: your GPS triangulates your location using the relative motions of satellites. Those satellites emit signals, which are then blue-shifted or red-shifted because they are moving toward or away from us. However, these signals are ALSO blueshifted because they are shining downward into the Earth's gravity well (because these satellites are in orbit, and you aren't) which means that they pick up energy as they descend. Yet, the signals are still moving at the same speed, which is the speed of light, and in the satellite's frame of reference the frequency at which they are emitted is determined by the current in the satellite's antenna, which has a set time frequency. The only way that you can observe a different (and higher) frequency is if time is moving more slowly for you down on Earth than it does for the satellites up in space. Hence, time dilation.

We know this because if you tried to use GPS without the general relativistic equations, and relied on special relativity, then your GPS receiver would get your location wrong.

Having not seen Interstellar, I cannot say for certain what is going on, but from what I have read about the movie, the distant planet is orbiting a black hole (thus deep in its gravity well), with the consequence that time is much slower there than it is on Earth, creating time dilation.