stead is a somewhat old word that means "standing or place". You find it in older phrases like the one you mentioned, and in compound words: homestead (can mean home or the land), instead (in place of)... there are others. You'll see it in some town names, as well.

In this situation, "to be in good stead" means to be "in a good position" or "to have a good reputation with someone."

He was well regarded by his teachers. In good standing. They hold him in high esteem. They think well of him.