Full Idea
A truth assignment 'satisfies' a formula, or set of formulae, if it evaluates as True when all of its components have been assigned truth values.
Clarification
a 'wff' is a well-formed formula
Gist of Idea
A truth assignment to the components of a wff 'satisfy' it if the wff is then True
Source
Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.2)
Book Reference
Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.23
A Reaction
[very roughly what Enderton says!] The concept becomes most significant when a large set of wff's is pronounced 'satisfied' after a truth assignment leads to them all being true.