Does it have square stems? If so it's of the mint family, probably oregano or marjoram.

The stems are round, fuzzy and soft (not woody.) The mother plant doesn't resemble any herbs I've grown before, but I am by no means an expert.

Perhaps Cuban Oregano, Plectranthus amboinicus. P amboinicus

Or "Vick's plant" Plectranthus tomentosa.

Plectranthus have square stems.

Some might. But I've just been to check my P fruticosus. Round stems. And this one - P amboinicus.

Many members of the Lamiaceae do have square stems but it is by no means universal in the family.

Please put it somewhere out of your cat's reach until you find out. My cat loved my tomato plant leaves when I was growing them inside ( I found out later they were poisonous to him) and he loved my African violet leaves. Both have fuzzy/hairy leaves.

That's funny zzackey, my cats have never bothered my African violet leaves but they do like to eat spider plants!