Pulcheria is Raskolnikov and Dounia's mom. She loves her little Raskolnikov and would do anything for him. Even, according to him, push her daughter into the arms of the cruel Pyotr Petrovitch Luzhin, whose money and power might help Raskolnikov get ahead in the world.
We think Raskolnikov judges his mother too quickly on that count. After all, she makes it clear in the letter that she really does think Luzhin is a bum. She knew he would react strongly to the letter and probably step in and stop the marriage. She is a proud woman and a bit of a snob. She admits she was happy when Raskolnikov's first girlfriend, Natalya Yegorovna, died, and she is rude to Sonia because she's worried Sonia will snag her boy. Eventually though, she approves of the relationship – not that anybody much cares.
Despite her flaws, she is also very much associated with the word "love." We find "love" more times in her letter than in the whole rest of the novel. Her intense love for her son, though, is many ways her downfall.
Though Raskolnikov moves between cruelty and kindness with his mother, she just can't understand why he's so strange. Dounia and Razumihin take pains to hide his crimes from her, but Pulcheria knows full well what's going on, even if she doesn't talk about it. This is why she clings so tightly to the story of Raskolnikov rescuing children from a burning building, and even goes to see those children.
If her son is a killer, that makes her a bad mother in her mind, and so she has to hang on to any bit of good she can find to keep her sanity. Unfortunately, it's not enough. The combination of being aware of Raskolnikov's crime and his absence from her life pretty much kills her. She dies without ever seeing her son again.