'quarters' is a term used for a type of accommodation that is not that fancy, but is good enough for temporary workers or perhaps others staying short-term like guests or tourists. The key idea is this accommodation has all the facilities necessary for someone to stay, but it may not be fancy. It's possible it is very nice, but usually it means it is basic in some way - just the minimum. Often only sleeping facilities with only very basic kitchen facilities but sometimes not even that. If you say 'informal quarters in a guesthouse', it implies there are several sleeping facilities for different groups of people, but they likely share the one bathroom and the one kitchen. Otherwise, if there is a bath/kitchen facility for each 'sleeping facility' then that facility will be very minimal.

These days, homes and guest houses use a style of writing to create a particular ambience. It simply means a nice place to stay. The key is the word informal....A place you can relax without rigid rules, dress code or timetable.

I don't have the rest of the context of this text, but based solely of the sentence, I would interpret the "informal quarters" as a fancy way of saying 'living space'. So I think this would refer mainly to areas of the house like the living/dining room, where people tend to congregate in informal settings to relax or catch up I hope that answers your question. If you'd like to practice speaking or need help with grammar/vocab, I'd be happy to help you develop a study plan. Feel free to look at my teaching profile and class offerings and send me a message if you think I can help you!