The adverb awhile (one word) means for a short time: "Stay awhile."
The noun phrase a while (two words) refers to a period of time: "I sat for a while and waited."
Also see the usage note below.
- Before removing the radiator cap, wait awhile for the engine to cool.
- I haven't been to a football game in a long while.
"Awhile is an adverb, with the same meaning as the adverbial prepositional phrase for a while: Let's rest awhile; Let's rest for a while. When for a while cannot be substituted for awhile, awhile should be a while: spend a while with me. When for occurs, awhile should not follow; Stay for awhile should be Stay for a while or Stay awhile."
(Edward Johnson, The Handbook of Good English. Washington Square Press, 1991)
Practice:(a) "Life's short. If you don't look around once in _____ you might miss it." (Ferris Bueller)
(b) Merdine invited me to stay ____ longer, but it was getting late.