Full Idea
Non-truth-functional accounts agree that 'If A,B' is false when A is true and B is false; and that it is sometimes true for the other three combinations of truth-values; but they deny that the conditional is always true in each of these three cases.
Gist of Idea
Non-truth-functionalist say 'If A,B' is false if A is T and B is F, but deny that is always true for TT,FT and FF
Source
Dorothy Edgington (Conditionals (Stanf) [2006], 2.1)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.3
A Reaction
Truth-functional connectives like 'and' and 'or' don't add any truth-conditions to the values of the propositions, but 'If...then' seems to assert a relationship that goes beyond its component propositions, so non-truth-functionalists are right.