Basically, a smart home is a home where certain aspects are programmed to happen automatically. This can be for example lightning, heating, shutters, entertainment systems such as TV and radio or protection systems such as a camera. Your appliances are all connected to a software, which you can use to control them. There are quite a few different systems on the market by now, each with their specific advantages and challenges. So if you want to get one, I would do some research first. Alternatively, you can control certain systems such as cameras via your phone. I am not sure if I would already call that a smart home, though. Also, I am not sure what exactly you mean by „control your pets“? Can you elaborate on that?
I am by no means an expert on the topic, I just did some research after reading an article on IP cameras a while ago when looking for a new camera to protect my home. (If you want to read it as well, you can find it here:
https://www.fotospring.de/ip-camera-test/ It’s in German, but you can easily translate it with Google or DeepL, if you’re interested). Most of these products are controlled via an App, so I got to thinking what else I could control with my phone and down the Internet rabbit hole I went.