A Normal House is a house where all the "normal" citizens live in the episode "Not Normal."
They are all blue with a white door flanked by two bushes, and two windows. The lawn is green and closed off by a white fence. It only appeared in Not Normal. SpongeBob's Normal House is orange, and the only shot of the interior shows that it has beige walls and orange carpet.
Although this is regarded as a "normal" home, most fish live in metal apartment-like buildings, not homes like these.