Merge

In minimalism, Merge is the structure-building operation. It takes two elements from the numeration, combines them and assigns a label to the structure thus formed; the label is identical to one of the elements that are merged.

Example
Take for instance Merge of a direct object with a verb:

/\                    Merge         /  \ build + airplanes --->   build  airplaines

build /\ label assignment       /  \ >  build  airplaines

The label determines the syntactic properties of this structure; in this sense, the label is equivalent to the notion of projection. The trees are shorthand for set-theoretic notations: (i) is shorthand for (ii):

(i)   build         (ii) {build, {build, airplanes}} /\       /  \    build  airplaines

Comments
Chomsky uses the term substition for instances of Merge that are not adjunction. Adjuncts are also attached by means of Merge; the difference with non-adjunction structures is reflected in slightly different notations; adjunction of A to B results in:

{>, {A,B}} (Chomsky 1995)

or:

{B, } (Chomsky 1998) 

Chomsky (1998) proposes to make label assigment dependent on the selection properties of the elements that are being merged. In the case of substitution, the selector always projects. In adjunction structures, the element that projects is the one that is being adjoined to.

Link
Utrecht Lexicon of Linguistics