The term complement describes that post-head (verb) sentence element that completes the meaning of the phrase.
Pre-head string | Head | Post-head string | |
Peter | plays | the piano | |
Peter | plays | the piano | beautifully. |
Peter | likes | coffee | with milk |
complement | adjunct |
Generally, complements differ from adjuncts in that complements are obligatory, adjuncts are optional. Adjuncts are stackable, i.e. you can stack more multiple adjuncts onto one another:
Peter | plays | the piano | beautifully | in the living room. |
On the difference between complements and adjuncts, see: http://www.ucl.ac.uk/internet-grammar/phfunc/compare.htm