Full Idea
A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part.
Clarification
'Unsaturated' functions contain variables but not actual references
Gist of Idea
A concept is a function whose value is always a truth-value
Source
Gottlob Frege (Function and Concept [1891], p.30)
Book Reference
Frege,Gottlob: 'Translations from the Writings of Gottlob Frege', ed/tr. Geach,P/Black,M [Blackwell 1980], p.30
A Reaction
So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable.