The actual intuition for how URANS works seems a bit murky. I guess I conceptualise it like this: when we do Reynolds decomposition, we think of velocity as a mean component plus a fluctuating component like U=u+u'. The fluctuating component is parameterised to be represented by some turbulence model, eg k-epsilon. In regular RANS, that mean component is constant. When we move to URANS, we allow that mean component to change over time, while still modelling all of the fluctuating component