I have post residue urine of 301.97 (normal range 30 ml). My doctor (nephrologist) wants me to see a urologist? What doe it mean? How serious is this?

Not emptying. It means you are not emptying your bladder which indicates either a bladder outlet obstruction such as by prostate or that your bladder musculature is not contracting strongly enough. See a urologist for diagnosis and treatment. Good luck.
Post void residual. A high post void bladder residual means that your are not emptying your bladder completely. There should be less than 30 cc in bladder post void, certainly no more than 50 cc. Normal bladder capacity is about 400 cc, so your PVR is high. The urologist needs to determine why and fix it. Perhaps it is your prostate or urethra or a bladder function problem. You need dx and rx.
Risk of infection. Post-voiding residual urine predisposes one to urinary infection and it is important to ascertain the cause for a proper treatment. A urologist is an appropriate specialist for the disorder.