As a dependent clause, a non-finite clause plays some kind of grammatical role within a larger clause that contains it. What this role can be, and what the consequent meaning is, depends on the type of non-finite verb involved, the constructions allowed by the grammar of the language in question, and the meanings of those constructions in that language. Some examples are noted below:
To live is to suffer in silence. (infinitival clauses used as subject and object)
We went there to collect our computers. (infinitival clause used as an adverbial of purpose)
They were sitting quietly. (participial clause used as verb complement to express progressive aspect)
The man sitting quietly is the man to watch. (participial clause used as noun modifier)
Well beaten, we slumped back to the dressing room. (participial clause used as nominative absolute)
I like rescuing wasps. (gerund-participial clause used as a noun phrase)
Carthago delenda est ("Carthage must be destroyed"; Latin gerundive used as a predicative expression)
For more details of the use of such clauses in English, see Uses of English verb forms: Uses of non-finite verbs, and English passive voice.