Ok, she's really more of a plot point than an actual character in the story. The mom of the girl that Kovalev has been flirting with but not proposing marriage to (back in the day when you didn't make eyes at a girl you weren't going to marry), Madame Podtochina is all up in Kovalev's business trying to make the match happen.
But here's something funny: Kovalev may be after the daughter, but it's the mom who keeps popping up. In a way, it's like she's the one seducing Kovalev into the family.
Add in the fact that he's 42 years old, and so probably way closer in age to Madame Podtochina than her daughter (since in those days dudes used to marry really young women, we're going to guess the daughter is in her early 20s at the oldest), and what we've got is a weirdly dark sexual undercurrent that doesn't really get spelled out in the story but is totes there nonetheless.