“What's with the yawning? Were you out all night partying?”
Your coworker is yawning and looks tired. You are friends with this person, so you want to tease him. You smile and ask this.
What's with the yawning? Were you out all night partying?
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"What's with ___?" is a casual way to ask why something is happening. For example, if you come into work and your boss has a big vase of flowers sitting on her desk, you can ask:
What's with the flowers?
This means "Why do you have flowers on your desk?"
"Yawning" is what people do when they are sleepy. When you yawn, you open your mouth wide and take in a deep breath.
People sometimes use the phrase "out all night drinking" or "out all night partying" to describe someone not coming home because they are drinking or at a party.
You can also use "out all night" by itself:
I was out all night.
When you use "party" as a verb, it sounds wild. "I was partying all night last night" sounds like you were drinking a lot and maybe using drugs.
So when the speaker in the example says "Were you out all night partying?" the listener understands that it was probably a joke (unless he really is someone who has very wild party behavior).
The more usual and calm-sounding way to use "party" is "have a party" or "go to a party":
Did you go to a party last night?