Okay so here's the thing.
You're hired to do this job by this woman named Grace. And it's a very particular job, and you know she could do it with a machine but she needs this personal touch. And you follow along with it. It's pretty fun at times, after all. You do get this sense that she's just going through the motions with this, just meeting her needs and not much else, but that's not your problem or your business. And there are some odd things about it - she's a little pushy, and sometimes you find some art around her place that you presume is from someone she used to be in a relationship with, but that's not really your place to question. When things start to heat up is when you get into a fight over her wanting you to break ties with one of your friends. You both do and say some regrettable things, and you end up out of her reach for a bit, going through the motions and all that.
Then, one day, you meet this other guy - let's call him Will. He's charming and he seems to have some sort of plan for his life, so you start hanging with him for a while. And then you run into her again. Grace. And she is pissed about this whole arrangement and the bad blood between you two, so you decide a little petty revenge is in order and to make a long story short Will gets the deed to her house. Then Will starts getting ideas, and Will? He's not so good when he gets ideas. He ends up kicking you both out onto the street, and now you're down and out together.
And you get to talking - well, you don't talk all that much, you've never been the talking type, but she talks a lot. You finally learn her real name - Carol - and her past. She apparently used to be in this thing with this guy back in the day who she had a really toxic relationship with that just... sucked the fun out of the sort of things you'd do together for her. He was this older guy, really just an arrogant asshole who took advantage of her and ever since she's been stuck like this.
At any rate, you eventually manage to get back to Will, and you rough him up a little until you can manage to finagle things back into the proper place. With Carol back at the head of the house, things seem a little better, back in their proper place. The thing is, Carol's learned a little since you started this whole arrangement. She doesn't think that this will ever work out - not like it used to. So, instead of being possessive, she lets you go. She says that she doesn't feel anything for you anymore but that can't really be true. She sings to you as you leave, and sends you that old friend's number as a way of making up for that old fight.
And that's why in Portal 3 you're going to march back up to that door, go back down into Aperture Labs, and fuck that robot.