A nephrologist is a person specializing in renal medicine, which is, more or less, looking after the kidneys. They used to be called just "renal physicians" but there seems to be a movement recently for them to rename themselves as nephrologists.
Most healthy people will never have to see a nephrologist - and that's a good thing for if there is some trouble with your kidneys, you had better hope the damage isn't too serious and that the process does not perpetuate ... because the consequences of renal failure to anyone's well-being is pretty miserable.