Masaki was Isshin's wife, the woman he loved, and mother to his children. We actually know very little about her - which isn't surprising seeing as how she died several years prior to the start of Bleach. At the time, her death was considered an accident, even while Ichigo blamed himself for it. Pause for one lone tear. However, in volume three, we find out that a Hollow known as Grand Fisher was the cause of her death. He lures humans with high spiritual energy by using a human shaped doll and putting the person in a dangerous position - like the girl Ichigo thought he saw at the side of a river and ran to save.
Ichigo, even at age nine, already felt the need to protect everyone. However, from his mother's point of view (as far as we know), all she saw was Ichigo running toward the edge of a river. She ran after him, and not even Ichigo was sure what happened next. All he knew back then was that there was blood, his mother was dead, and the girl he had been attempting to save had disappeared. Only years later, once he's gained his Shinigami powers that he discovers what really happened. It's certainly a traumatic experience that would affect anyone deeply.
Masaki was the centre of the Kurosaki family. As Ichigo says, they all orbited around her and loved her dearly. Her death affected them all drastically. Ichigo went from a smiley crybaby to the somewhat surly character we know and love. Karin also changed from a crybaby to a tough little girl. Yuzu, while still being something of a crybaby, tried to fill the void by taking over household chores and cooking for the rest of them. Isshin...well, we don't know what he was like before Masaki died, so it's hard to tell. There's no doubting that he loved, and still loves her greatly. And, knowing now a little something about his past, Isshin most likely knew at the time of Masaki's death that it was caused by Grand Fisher. But at that point he had no Shinigami powers, and as he comments later to Urahara, his inability to save Masaki was something he couldn't get over.
Isshin has some really nice moments at the end of volume 3. Aside from looking hot with a cigeratte (yes, Masaki, we fangirls concur), his whole attitude with Ichigo, and the way he speaks of Masaki is really wonderful. It's bittersweet nostalgia, and yet he's proud to know that the woman he loved would die trying to save her son. That's who she was, and he wouldn't have changed her for the world.
While Ichigo does defeat Grand Fisher, the Hollow runs away before Ichigo can kill him. However, much later in the story, Isshin makes his Shinigami debut and takes down Grand Fisher in one hit. Emphasised because Grand Fisher was at this point an Arrancar, albeit an incomplete one. Isshin may have had his revenge, but it still doesn't bring back his wife.
There are a couple of unexplained mysterious surrounding the day Masaki died. The main one being the fact that Ichigo wasn't killed. Just as he reached the girl standing by the riverside, she tipped forward, and he tried to grab her. Masaki obviously got to him in time, because Ichigo awakens on the riverbank, with his mother's body on top of him - shielding him. If Masaki was a normal human, she could not have seen the girl. However, then she would also not have been able to defend herself or Ichigo against Grand Fisher. So it could be assumed that Ichigo, even as a child, had a much higher spiritual energy than Masaki, so Grand Fisher would still have killed Ichigo after her, or even before - the boy would have been more appetising for him.
Unless Masaki was able to defend herself against the Hollow. After all, Grand Fisher does run away when he is losing a battle. But that would suggest that Masaki was either a Shinigami or a Quincy. If she was a Quincy, it...really makes Ichigo a little bit of everything, and honestly, I don't like that idea very much. Quincy things = Ishida's story, and not to be mixed with Ichigo's. However, Isshin and Ryuuken, Ishida's father, appear to have some kind of link, despite the fact that they clearly dislike each other, more so than the Ishida/Ichigo rivalry thing. Could this link have been Masaki - either as part of the Quincy, or as some doctor love triangle?
Now, if Masaki was a Shinigami, that would make Ichigo a pureblood. Which might go toward explaining his power, although technically I would have thought that would just have put him on par with nobles born in Soul Society like Byakuya. It could also make for romantic!Shinigami runaway story starring Isshin and Masaki, but that just doesn't seem right. It sounds like something Orihime would daydream about. Mechas optional.
Another question that pops up is just when did Masaki die? When Isshin and Ichigo are speaking in front of her grave, Isshin comments that it's already been ten years since she died. Ichigo is not impressed and says that it's been six years. Perhaps this is completely off the mark, but getting something like that so wrong doesn't seem like something Isshin would do. Not on this subject. What's more interesting is that, later on, Isshin mentions to Urahara that he first encountered Arrancar around ten years ago. And ten years ago, Isshin was without Shinigami powers and would have been in a spot of bother if an Arrancar was targeting him. But the circumstances to this encounter are unknown, so we have no idea of knowing if Isshin's verbal slip was accidental or if there's something else to Masaki and her death.
We have no answers to these questions right now, all we can do is speculate on Kubo's great plan and hope we get answers someday.