What does GLaDOS mean with "One day they woke me up"?

Solution 1:

They mean the day she was initialized. During the game Cave Johnson mentions that he wants his team to take the personality of Caroline and put her in a computer.

Since GLaDOS exists, we must assume that his team succeeded in doing this. So they started building her and putting Caroline's personality into GLaDOS. Then, one day they woke her up so she could live forever and feel bad for Chell because it'll never happen to her.

Solution 2:

This started when Cave got his disease from moon dust. He wanted to live longer, so he asked his engineers to build something that he could transfer his mind into. He also ordered that if he passed away before the machine was completed, Caroline would be transferred instead. Since he does, indeed die before it was built, Caroline was forced to be transferred into the machine.

A long time later, GLaDOS(Caroline) was activated. And that's why she says that line.

Also, there are some disturbing lines from the game which were cut telling how Caroline was transferred, only a few of these lines are found in the game files.

The disturbing part starts at 0:28. Hope my post helps.

Solution 3:

Caroline was the assistant of Cave Johnson. He had Caroline's mind put into the computer. When they turned her on she flooded the complex with a deadly nerve toxin. That is why there is no personnel and that is what the song means by one day they woke me up.