Mrs. Croft is a big reminder to our narrator of the concept of responsibility, specifically his duties to her, as a young man in a new country:
At times I came downstairs before going to sleep, to make sure she was sitting upright on the bench, or was safe in her bedroom. On Fridays I made sure to put the rent in her hands. There was nothing I could do for her beyond these simple gestures. I was not her son, and apart from those eight dollars, I owed her nothing. (TFC 96)
In our humble opinion, the narrator seems like he's already a really conscientious guy, checking in on Mrs. Croft the way he does. Maybe you can tell, though, that he feels like he's not doing enough.
Is he just a really nice guy? Or is there something else going on? Here's our bet: it's all about the mother.
I was mortified. I had assumed Mrs. Croft was in her eighties, perhaps as old as ninety. I had never known a person who had lived for over a century. That this person was a widow who lived alone mortified me further still. It was widowhood that had driven my own mother insane. (TFC 92)
Mrs. Croft is a reminder of his mother, who eventually died from her grief.
Worse—Mrs. Croft isn't just a simple reminder. She actually brings up the fear that the whole thing might happen again—a death that the narrator has to be responsible for since no one else is really there. He might be forced to relive these final memories of his mother:
Nearly six years ago, before leaving for London, I had watched her die on that bed, had found her playing with her excrement in her final days. Before wecremated her I had cleaned each of her fingernails with a hairpin, and then, because my brother could not bear it, I had assumed the role of eldest son, and had touched the flame to her temple, to release her tormented soul to heaven. (TFC 39)
Pretty harrowing memories, if you ask us.
In fact, they kind of make Mrs. Croft more than just a symbol of a son's burden and a son's duty; she's really more like a symbol of death—only living.