It's told incredibly subtlety, which I think was the best choice.
So the obvious thing shown is Caroline (the basis of GLADoS' personality) and Cave were involved with each other. You also can know from the first game and something that you can find hidden in the second game that Chell was in the facility when this all happened because she was visiting on "Bring your child to work day", which means Chell's mother was an employee of Aperture. Moreso you can find in the area in Portal 2 with all the science fair exhibits the children held on take-child-to-work day, a potato power exhibit that's grown out of control, and if you look at the label of who's exhibit it is, it's Chell's. Of course some irony later when GLADoS needs to be powered by a potato battery as that was Cell's science fair project.
GLADoS at multiple times says things to get a rise out of Chell, including that she's adopted and that her mother was a test subject. Chell is not the same race as Cave Johnson or Caronline, and Caroline did ultimately become a test subject to make GLADoS. When GLADoS is overwhelmed by the emotions of Caroline, she says in a tender way to Chell that it's good she's awake. GLADoS also mentions that Caroline was a lot like Chell.
In the background of Cave and Caroline's photo you can see Chell just barely in the back of the frame:
Both of the ending songs heavily allude to it. The opera song with the turrets at the end especially, which is the song, "Oh my daughter" in Italian. The lyrics in English are:
While GLADoS puts up a front of making Chell leave because she's sick of her always not dying, the real reason is probably after regaining Caroline's memories and feelings, she wanted Chell to go on to live.