0.90c what unit is (c) referring to?

c is the symbol of the speed of light in vacuum. 0.9c means 90% of the speed of light in vacuum.

The unit of c is meter/second (m/s).

c = speed of light  I just wanted to comment that the text you got this from is doing a poor job of explaining the concept of relativity.  The point it is missing, which is entirely essential to understanding relativity, is that given two observers who are moving at constant, relative velocity with respect to each other, both will observe the other's clock as running slower as neither can tell who is at rest and who is in motion.  So in the train example, Claire sees Anne's clock as running slower, but Anne also sees Claire's clock as running slower compared to Anne's.  The reason is that there is no test either can perform that would allow them to say who is really moving and who is at rest.  I know it is hard to imagine a train station sitting on the earth being the thing in motion (especially at 0.9c) but from a pure physics viewpoint, this is the case.  If you don't understand this, then the Twin Paradox will not make sense to you.

c in that context would be the same c of E=mc^2; the speed of light.