In the 2014 film Interstellar, why does the spacecraft Endurance spin? I think it really has to do something with physics?
It rotates to create artificial gravity
A rotating space station is a known concept (apparently Tsiolkovsky thought about it in the very beginning of 20th century). It uses the rotation to induce a centripetal (acting towards the centre) acceleration on the people inside.
In order for a body to stay in motion with constant speed in a circular path with radius R, it must have an acceleration equal to the square of its linear speed divided by the radius R (or the square of its angular speed multiplied by the radius).
This acceleration is actually caused by the normal force exerted by the floor of the station on the people - the people inside would be hurled into space, but the floor keeps them in the circular path, so they feel an acceleration which is similar to the acceleration due to gravity.
From the Wired article
As to why it's needed at all - remember that Endurance is not a fast flier. It's supposed to be in space for a long time (Romilly spent 23 years there), and being subjected to weightlessness for a long time bone decay occurs. The simplest solution is to take gravity with you, and this is a plausible way to do that (though we are yet to see any such stations in real life).
Read about various ways of achieving artificial gravity (hat tip to Johnny Bones)
Might want to revisit uniform circular motion too.
See also Larry Niven's Ringworld which applies this concept to a whole world.