Finite verbs are verbs that show tense and agree with the subject in person and number. They can stand alone as the main verb in a sentence, indicating actions or states of being. For example, in the sentence "She runs every morning," the verb "runs" is finite because it is tied to the subject "She" and indicates present tense. In contrast, non-finite verbs, such as infinitives and gerunds, do not show tense or agree with the subject. They often function as nouns, adjectives, or adverbs. For instance, in "Running is fun," the word "Running" is a non-finite verb acting as the subject of the sentence.