|Definition - In a post-creole community, it is the dialect that most closely resembles the creole. It is also the lowest register of a spoken language.|
Etymology - The term was coined by Derek Bickerton by — I would guess — joining the combining form basi, base, with the word dialect.
Oxford English Dictionary - Its first citation is from 1977:
"Speakers in a post-creole community are triply pressured:
to avoid the basilect, to acquire the acrolect, and to vary the mesolect."
(Language LIII. 330 )