Despite its importance, the role of sleep remains a mystery.

Literal

Sleep [topic-は] important [copula-である-although-にもかかわらず], its role [topic-は] mystery [copula-である].

Formal academic writing register. Two notable features. である is the formal/written copula, replacing だ in essays, papers, and journalistic prose. ~にもかかわらず ('despite, in spite of') is the formal concessive conjunction; the casual equivalent is ~のに. The whole sentence is the classic 'X yet Y' contrastive structure typical of expository writing.