What an absolute crock.
The question is "why do we yawn", not "what is a yawn". This asinine paragraph is talking about why we open our mouths to yawn? WTF, that's what yawning IS.
And it also incorrectly asserts that yawns are associated with a deep breath. You hear this all the time, but a yawn does NOT induce a deep breath; they may sometimes happen at the same time, or perhaps people simply feel a yawn is also a good time to take a sighing breath. But a yawn is limited to the musculature of the jaw, and that's it. Try it. You do not need a take a breath when yawning; it has nothing to do with it.