A finite verb is a verb which serves as a predicate verb (i.e., it has a subject and has the ability to function as the root of an independent clause). Most of verbs can present in a finite and non-finite form (where the verb does not serve as a predicate and cannot support an independent clause).
The subject of a finite verb can be stated or implied.
In English the role of a finite verb is subtle, but in other languages, the finite form of a verb can state gender, person (e.g., first, second, third), number, tense, aspect, mood, or voice. Generally English does not change its verbs for many of these instances.