In Saussurean terms, a syntagm is a structural sequence, where each sign follows another in a string, for example words in a sentence. The rules governing which word may follow another are defined by the grammar of the language.
The words the+cat+sat+on+the+mat stand in syntagmatic relationship to one another and cannot be rearranged arbitrarily without losing the meaning of the sentence.
Linguistic analyses which focus on collocation (Firth, 1957) operate at the syntagmatic level, as opposed to the paradigmatic level, which is involved in studies of synonymy and antonymy, for example. Firth was not a structural linguist, believing that meaning and context are essential to linguistic interpretation.
Classroom illustration: Collocations