Some verbs require specific things in order to make sense and be grammatically correct.
⇒ things that you can't leave out are called complements.
⇒ things that are optional are called adjuncts.
For example, every sentence needs a subject - someone or something that performs the action. The only exception is the imperative (command form), where the subject is implied: i.e. "Komm!" (Come!)
Complements can be individual words, phrases, or clauses.
Here are the different types of complements a verb can require
⇒ "Der Mann," "dem Kind"" and "den Ball" are all complements. Without all of them, the sentence doesn't make sense. For example, if I said "The man gave" it wouldn't make sense. What did he give?!?!?
⇒ „jetzt“ is an adjunct - it is just extra information. Leaving it out still leaves a grammatically correct sentence that makes sense.
⇒ „Der Mann“ can't be left out. It's a complement.
⇒ „mit einem Geschenk“ and „auf seine Tochter“ are extra pieces of information - they could be left out and the sentence would still make sense. "The man waits" is a full sentence that makes sense.
All the info you need for the various complements in German: