Full Idea
Here is a partial definition of the concept of satisfaction: John and Peter satisfy the sentential function 'X and Y are brothers' if and only if John and Peter are brothers.
Gist of Idea
A sentence is satisfied when we can assert the sentence when the variables are assigned
Source
Alfred Tarski (The Establishment of Scientific Semantics [1936], p.405)
Book Reference
Tarski,Alfred: 'Logic, Semantics, Meta-mathematics' [Hackett 1956], p.405
A Reaction
Satisfaction applies to open sentences and truth to closed sentences (with named objects). He uses the notion of total satisfaction to define truth. The example is a partial definition, not just an illustration.