Full Idea
Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions.
Gist of Idea
First-level functions have objects as arguments; second-level functions take functions as arguments
Source
Gottlob Frege (Function and Concept [1891], p.38)
Book Reference
Frege,Gottlob: 'Translations from the Writings of Gottlob Frege', ed/tr. Geach,P/Black,M [Blackwell 1980], p.38
A Reaction
In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions.