Connective

In semantics, connective is a logical operator which combines with one or more formulas to form a more complex formula.

Examples
Binary connectives, like &, v, -> and <->, combine with two formulas as in (i), the unary connective Neg combines with one formula as in (ii).

(i) Phi &  Psi		(and) Phi v  Psi		(or) Phi -> Psi	(if ... then ...) Phi <-> Psi	(... if and only if ...) (ii) Neg Phi		(not)

Comment
The truth-value of the complex formula is always a function (a truth-function) of the truth-values of the formulas Phi and Psi, which can be represented in a truth table.

Link
Utrecht Lexicon of Linguistics

Reference
Gamut, L.T.F. 1991. Logic, language, and meaning. Chicago: University of Chicago Press.