The ears come from the International Phonetic Alphabet, which language experts use to write down sounds. ʔ is the glottal stop, the short break in the middle of "uh-oh". ʕ is a throat sound from Arabic. Only their round shapes matter here.
The parts of ʕ•ᴥ•ʔ
ʕU+0295Latin letter pharyngeal voiced fricative. The left ear.
•U+2022Bullet. An eye.
ᴥU+1D25Latin letter ain. The snout.
ʔU+0294Latin letter glottal stop. The right ear.
Cats, dogs and bunnies
Many cat faces borrow letters from far apart. In ฅ^•ﻌ•^ฅ the paws are ฅ, a Thai letter that is no longer used in Thai writing. The mouth ﻌ is the Arabic letter ain, in the shape it takes in the middle of a word. Bunnies use ㅅ, the Korean letter for an s sound, as a little split lip.
Fish and bugs made of plain keys
These use only keys from a normal keyboard. They show on every phone and every app, even old ones.
You can't type ʕ and ʔ on most keyboards, so copy ʕ•ᴥ•ʔ from this page. On a phone, save it as a text shortcut, for example "bear", and your keyboard will offer it when you type that word.
What is the ᴥ character?
It is LATIN LETTER AIN, U+1D25, from a block of letters made for writing sounds. In text faces it is the snout of a bear or a dog.
Can I use animal faces in a username?
Some games and apps allow only letters and numbers, so the face is removed or the name is refused. Faces made only of plain keys, like =^..^=, have the best chance.