Adjuncts are one of the five major elements of clause structure. The other four are subject (s), verb (v), object (o) and complement (c). Adjuncts (a) are some times called adverbials.
An adjunct is a phrase which is not necessary to the structure of the clause, but which adds some extra meaning to it.
In the sentence They waited outside for ages, the phrases outside and for ages add extra meaning to waited. They tell us where, and for how long, the people waited. They are adjuncts:
[S]They [V]waited [A]outside [A]for ages.
[S][V]I kept [O]a copy of the letter [A]in my desk.
[S]She [A]quickly [V]realised [O]her mistake.
[A]Suddenly, [S]it [V]started to rain.
Adjuncts and complements are different. An adjunct is not necessary, and adds extra information. A complement is necessary in order to complete the meaning:
[S]He [V]put [O]some salt [C]in the soup.
The verb put must have a complement saying where something is put. Without the complement (in the soup), the clause would not be complete. We cannot just say He put some salt.
Adjuncts are different from postmodifiers in noun phrases. An adjunct adds extra information to a clause. A postmodifier tells us more about the noun (n):
[S]They [V]’ve closed [N] that restaurant [postmodifier]on Market Street.
on Market Street is a postmodifier. It is part of the object noun phrase. It tells us which restaurant we are talking about.
