A self catering apartment, hotel room, hostel, vacation place, etc, is one where guests have facilities for making their own meals and cooking, and are allowed to do so.
Normally a hotel might give guests a kettle and some coffee/tea, maybe some biscuits, and usually a dining room with menu, sometimes also room service.
By contrast, a self catering apartment/room might have a small "galley kitchen" - for example a fridge, a hob or cooker, or microwave, some basic kitchenware - plates, cups, bowls, cutlery, a sink suitable for washing up, and so on. The self catering facility can be in the room/apartment itself, or a communal shared kitchen facility for all visitors. A galley kitchen isn't large, it fits in the corner of an ordinary hotel room.
We went to Spain some time ago, and the hotel had self catering apartments as well as a dining facility with buffet. We enjoyed the buffet breakfast most days but cooked our own fish and made our own salad from local bought produce, one evening, and ate it on the room's balcony. It was delicious!