"It is snowing."
yağıyor doesn't really mean anything on its own, you have to use it with different kinds of precipitation
yağmur yağıyor: it is raining
kar yağıyor: it is snowing
dolu yağıyor: it is hailing
so yes it is like falling, but only for rain snow and hail, for nothing else
Adding to this:
You can find "yağmak" in literature when referring to anything that falls from the sky: "Mermiler yağıyordu…" (Bullets were raining) etc. The idea is the same though.
O kar yağıyor means it is snowing right? Because the site says it can't put 'o' in. Why is that?
You can't use it in this sentence because 'o' is a pronoun.
"O kar yağıyor" would mean a specific thing is snowing, or "(S)he is snowing." It usually won't make sense, but I think you could use 'o' if you were referring to a snowglobe that has been shaken up and is now "snowing," or if you have a lot of dandruff and your head is "snowing." :P