What mean domestic?

In one of my classes today I gave a conversation activity. The students were supposed to ask eachother questions using a certain grammar topic. During conversation, one question that came up was, 'What pets did you used to have when you were a child?' And the conversation continued as follows:

Mahmoud: 'Teacher, what mean "pets"?'
Me: 'It's an animal you keep--'
Mahmoud: 'Ah, camel!'
Me: 'Heh, well--'
Omar: 'Teacher, what is a pet?'
Mahmoud: 'Like animal in your house, cat, dog, camel...'
Me: 'Do you keep a camel in your house?'
Saleh: 'Teacher, can I say falcon is a pet?'
Me: 'Yes, Saleh, you can say a falcon is a pet.'
Saleh: 'Ok. I have a falcon.'
Me: silently laughing to myself...