What does an enlarged kidney actually mean?

Could be nothing: Kidney size correlates some with the body size. However, a blockage of kidney makes it swell and be large but the diagnosis is not going to be an elarged kidney but an obstructed kidney. Another reason is early in diabetic kidney disease where the kidneys get bigger early then start slowly shrinking over the years. Usually patient has diabetes and protein increase in urine.

Swelling of kidney: Hydronephrosis (swollen kidney) is generally secondary to an obstruction in urinary tract resulting in hindrance of urine flow from the kidney.