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.
Below are some examples of finite verbs with the verb in bold for clarity. (Side note: while there may be multiple examples in each sentence, only one verb is highlighted for simplicity’s sake.)
Two months into my first Chinese course some 42 years ago, I was ready to give up, totally intimidated and overwhelmed by its grammar rules (or lack of them), five tones and pictographs. [CNN]
There are 164 grammars in England, with individual schools scattered across the country and others in selective areas such as Kent and Buckinghamshire, where pupils are offered places based on their abilities, which are assessed by an 11-plus examination. [The Guardian]
Once it touches a person, it clings like blood stains on Lady Macbeth’s hands. [Toronto Star]
The University of Queensland is an edX partner, along with institutions including the University of California, Berkeley, the University of Texas System, Georgetown University, McGill University, École Polytechnique Fédérale de Lausanne, University of Toronto, and the Australian National University. [Business Insider Australia]