Hi,No wonder that those question surface fairly often- boarding houses were as obvious to XIX century readers as horse was to XVII century Poles but for modern day readers a lot of the context is missing.
Most of my sources are not in English so apologizes in advance for using literary examples since they can be the most familiar with.
The Industrial Revolution revolutionized the society all over the world. While cities were always a magnet for migration, XIX century saw a population explosion for cities.St Petersurg- a major trade and industrial hub, center of culture and education was no exception- from rich country nobles, young people trying to make it big to poorest ones trying to survive.
Supply followed the demand and in the middle of XIX century person looking for place to stay for a long time could chose from variety of accommodation tailored to their social standings and thickness of wallets. Let me exclude working and upper class and focus on our middle ones.
So where our Raskolnikov is standing? While he often describes himself as poor even narration shows us that he is not destitute like Marmeladovs - he has an income from writing (mainly letters to his mother, but still). With his background as an improvised noble and education he is a member of intelligentsia - for a lack of better term you can think about him as an struggling white collar.
Surprisingly, renting a flat was not the most common option for single man and woman. Unless you were really rich or already established in profession and could afford qualified household staff that was not an option- even with servants managing household - budgeting, planning groceries, managing various labor-intensive tasks like washing- was seen as an full time woman job. Unless Raskolnikov lived with his mother and sister, that kind of arrangement was beyond his reach. Doing all tasks by himself would be too time-consuming and worse- socially unacceptable.
Luckily, the market offered a place for this ever-growing class- a boarding house. Those establishments varied greatly, from renting beds in rooms to elegant ones like 221b Baker Street, but one thing in common for all of them was providing domestic service. Oftentimes they were run by middle class widows, since it was seen as a reputable source of income.
Most of them catered exclusively to male clientes-white collar women often resorted to unofficial arrangements where singe female lived with family renting her room and proving her reputation.
Don't let the meals and maid deceive you- Raskolnikovs house is a shabbier one. His trash was taken out, water was brought, cleaning was provided (either by landlady or hired "girl of all tasks") but he didn't have servant waiting him on foot. He didn't have kitchen nor running water- only samovar for tea- so he had either buy his dinner in cheap bar or stand or just pay for three meals a day cooked by his landlady.You can still find those in some parts of the world but in West they faded somewhere in the middle of XX century.
Further Reading
Życie prywatne Polaków w XIX wieku- multiple authors
Piękny Wiek XIX Borejsza Jerzy
A History of Private Life, Volume 4: From the Fires of Revolution to the Great War by Michelle Perrot