A finite clause contains a verb, subject, and context that clearly presents the tense of the clause. A non-finite clause, in comparison, does not clearly state the tense. For example:

• Finite clause: I danced with Emily last night.
• Non-finite clause: After we left, Emily and I stopped by the store.

In the finite clause, you don't need any other context to understand what's going on in the story. We know exactly what occurred, when, and with whom.

In the non-finite clause, you need more context to know when the event happened. Presumably, a clause that came before would indicate the event that came before, and its timing. This is a subordinate clause, depending on the context of the main clause to fit into the overall context of the story.

This is a good question. There are two basic points that need to be examined to answer your question. First, we need to define what a clause is. Second, we need to examine what a finite verb is.

Generally speaking a clause can be defined as something having a verb. An independent clause is a complete sentence and the dependent clause is subordinate to the main sentence.

"Jim walked" is Independent clause.

"While Jim walked, he saw a bird" is a dependent clause, as the clause "While Jim walked" depends on the main sentence.

A finite clause is a clause that has a verb with tense. The opposite of this would be a clause that has an infinitive (non-finite clause). The key is the tense of the verb. Let me give a few examples.

These two sentences are examples of a finite clause: "Jim played the piano" and "As Jim's mother called him, he played the piano."

An non-finite clause is as follows: "Jim loves to play the piano." Notice the verb "to play" is in the infinite, which does not have a tense.