Learn Hardcore Arabic (Levantine): البيطري عقم الحيوان الشارد. - The veterinarian neutered the stray animal.

ق in عقّم is often pronounced as a glottal stop ʔ in many urban Levantine accents, so you hear ʿaʔʔam.
Some speakers keep ق as q, so you may also hear ʿaqqam.
الشارد is written with ال, but because ش is a sun letter, it is pronounced esh-shāred or ash-shāred, not al-shāred.

What does البيطري mean exactly?

البيطري means the veterinarian or the vet.

It comes from the adjective meaning veterinary, but in actual use it often functions as a noun, just like English the vet.

So in this sentence, البيطري is the person doing the action.

What does عقّم mean here?

عقّم is the past tense verb, and here it means sterilized.

With animals, depending on context, it can be understood as: