What does it mean if I have protein in my urine? Is that a serious health issue?

Depends. A trace of protein in the urine in someone who is acutely sick with something isn't a concern. The most common cause of heavier proteinuria is orthostatic proteinuria, easily ruled out because the first-morning-voided urine is protein-free. Proteinuria of +1 or more should always be followed at least. A diabetic should have protein quantitated often since even small amounts are a warning.
Possibly. It depends on how much and why there is protein in your urine. Why did your doctor order this test? There are too many possibilities to discuss here but not all are serious.
Proteinuira . Protein in the urine can be a serious sign of renal failure when persistent, so this should be evaluated by a doctor. Sometimes, it can be normal to have some protein in the urine, especially when on high protein diets. You can tell there is probably protein in the urine when it is very foamy in the toilet.