Speakers will often use parenthetical phrases when they discuss a topic; these phrases are digressions which add some new thought or insight to the topic. They can be as simple as something like this and used often in conversation:
I saw Mrs. Pulaski at the grocery store yesterday. She (just to note) will have her shop open on Christmas Eve.
A parenthetical clause is similar in that it, too, is a digression. However, its grammatical construction involves a subject and a predicate, but does not always constitute a complete sentence. For example, a speaker could say something like this:
I saw Mrs. Pulaski (who, by the way, looks entirely different now) at the grocery store today.
All too often in conversation or discussion, parenthetical expressions do not really add much to the topic, but are simply a stray thought of the speaker. So, as a rule (especially when writing) one should avoid the use of such phrases and clauses. [Here is parenthetical phrase that I have used.]