Full Idea
'Γ |=' means 'Γ is a set of closed formulae, and there is no (standard) interpretation in which all of the formulae in Γ are true'. We abbreviate this last to 'Γ is inconsistent'.
Gist of Idea
A set of formulae is 'inconsistent' when there is no interpretation which can make them all true
Source
David Bostock (Intermediate Logic [1997], 4.5)
Book Reference
Bostock,David: 'Intermediate Logic' [OUP 1997], p.165
A Reaction
This is a semantic approach to inconsistency, in terms of truth, as opposed to saying that we cannot prove both p and ¬p. I take this to be closer to the true concept, since you need never have heard of 'proof' to understand 'inconsistent'.