Why do accretion disks spin?
Accretion disks spin because the material composing the disk is in orbit around an object.
Just like a planet orbits a star or a moon orbits a planet, disks of material can orbit some astrophysical object, such as a star or black hole.
Accretion disks are denoted as such due to the fact that there is high friction between the particles comprising the disk. This friction causes a loss of angular momentum, which causes the material "to move towards and onto" (accrete onto) its gravitational host. This is typically why an accretion disk will have a small tail that extends inward towards the body it is orbiting.
I personally have worked on accretion disk systems that result in type 1a supernova. A white dwarf star draws material from a nearby red dwarf and when it reaches the Chandrasekhar limit, it explodes spectacularly. There are physicists that study the magnetohydrodynamics of these systems to try and model the accretion disks that form. These types of supernova are very important as they act as time markers for looking back into the history of our universe. Knowing more about accretion disks can help us to predict when these supernova will go off, so that we can observe them.