what does the ““Heffinger puffs, white lingerus, cumula perspirants, and neb swirlums” mean？
Then, from above, a voice called down: “Quickly, the four types of rain clouds.”
“Heffinger puffs, white lingerus, cumula perspirants, and neb swirlums,” Skylar answered without hesitating.
does lingerus connect with linger, cumula connect with cumuliform，swirluma connect with swirl？

Question

Answer

Where did you read this?

I'm no cloud expert, but it does sound very fictional.

Answer

Yini is right. Those are made up (fictional) words. You're reading "The Familiars," and in books of that genre (fantasy) there are often many made up words. Especially if it is a book with magic in it. There are usually made up words for magic spells and other things. 
The words themselves are based on real words, though:
Heffinger = probably a made up name of whoever "discovered" them in the book.
puff = a fluffy whisp, like a cloud, or a puff of smoke.
white = cloud color
lingerus = sounds like fake Latin (example: a real cloud type is "cumulus" )
cumula prespirants = (see above, cumulus) and prespirant = making water (sweat is referred to as "perspiring")
neb = based on another real "cloud" word, "nebulous"
swirlums = swirl (clouds swirl in the sky) ums (a nonsense word ending, to make words sound cute)

Não perca a oportunidade de aprender uma língua no conforto da sua casa. Navegue pela nossa seleção de professores de línguas experientes e inscreva-se na sua primeira aula agora mesmo!