Specifically, a Poisson superalgebra is an (associative) superalgebra A together with a second product, a Lie superbracket such that (A, [·,·]) is a Lie superalgebra and the operator is a superderivation of A: Here,
This is one of two possible ways of "super"izing the Poisson algebra.
The other way is to define an antibracket algebra or Gerstenhaber algebra, used in the BRST and Batalin-Vilkovisky formalism.
The difference between these two is in the grading of the Lie bracket.
In the Poisson superalgebra, the grading of the bracket is zero: whereas in the Gerstenhaber algebra, the bracket decreases the grading by one: