To be "passed out" means to be asleep. However, "going to sleep" suggests something that you do on purpose. "Passing out" is something that happens without your control. A person "passes out" when he or she is extremely tired, drunk, or has been injured. Usually it happens in a place that's not normal to sleep in:
There was a guy passed out on a park bench. I was like, "What's he doing there?"
In the example above, when the mother says that her kids are "passed out", it means that they were really tired from playing outside in the sun all day, and they couldn't stay awake. Maybe they fell asleep really fast, or they're in a really deep sleep.
When you're talking about going to sleep, there are several stages like this:
go to sleep > be asleep > wake up > be awake
It's the same with "passing out":
pass out > be passed out > regain consciousness > be conscious
pass out > be passed out > wake up > be awake