what do the house sitters do during the day?

As Deb said, it all depends on the sitter and it's something you should discuss at the meet & greet, or before if that's a concern. I am a house sitter and I basically move into the client's home and use it as my base of operations during the entire stay. I'm retired so I don't work elsewhere. I come and go every few days to run errands, check on my house, go to church, etc. But I'm at the house the majority of the time, and always after dark, i.e. overnight. My primary concern is the care that the animal(s) need, and I always follow the routine given to me by the client.

That answer depends on who is the house sitter. Some sitters have jobs outside of pet care and some don't. You also may have questions about other time commitments (other pet care jobs, school, family, friends, etc .) to determine if it's the right match for the pet. It's best to discuss expectations before booking, either at the meet & greet or even before then, as each pet's needs and routines can differ greatly.