Put on a sock, then a shoe. Now try it the other way round: shoe, then sock. The results are different. Cube moves behave the same way. Turn R and then U and you get one cube; turn U and then R and you get a different one.

Mathematicians say two moves commute if doing them in either order gives the same result. R and U do not commute, because they both move some of the same pieces: the corner and edge where the right and top faces meet. Opposite faces such as R and L share no pieces at all, so they do commute: R L and L R give the same cube.