"Swell" is an outdated slang or colloquial word that means "really good." It was already dying out in the 1950s. However, one of the stock greetings people would write in each others' high school yearbooks was "Best of luck to a swell kid." When applied to a person, I think the closest word today would be "amazing." "Swell kid" means "amazing kid" or "nice kid" or "good kid."
"Swell" just means all-round good, not sophisticated or cool. You could compliment parents by saying "You must have raised him right, he's a swell kid."
"Swell" was considered to be nonstandard English and teachers didn't like it. An old joke of the period:
Teacher: "There are two words I never want to hear in this classroom. One is 'swell' and the other is 'lousy.'"
Student: "OK, what are the two words?"