Take Your Child To Work Day started as Take Your Daughter to Work Day. Once you remember that, its purpose and origins becomes obvious. Given that it was a feminist holiday meant to inspire women into ambitious white collar work, its origin is to me surprisingly late: 1992, with the first day being celebrated in 1993. It was invented by people working at the Ms. Foundation, a feminist organization originally associated with Ms. Magazine (the two have been completely separate since about 1987). The Take Your Daughter to Work program apparently didn't officially expand to boys until 2003. Just this year, Marie C. Wilson, who was president of the Ms. Foundation in 1992, gave an interview for Time about the origin of the holiday:

WILSON: [It came from] Carol Gilligan’s research looking at how adolescent girls started to lose their sense of who they were — thinking, talking and saying what they felt. You weren’t supposed to question boys. You weren’t supposed to know anything, so to speak.

[The Ms. Foundation] hired a great consultant, Nell Merlino, who told us a story that she had heard about a girl who was at a school that made arrangements for her to have an internship at a wonderful place in downtown New York. The girl went to the building, and she couldn’t go in. She was really intimidated, and she went home. They sent her a second time, and she got there, got a little further [inside the building], but she just couldn’t [go upstairs]. Finally, the person who had been working with her at the school just came with her and took her up to see the woman, and she got a great internship and lived happily ever after. Gilligan knew that it was important for women’s voices to support girls in keeping their sense of self in adolescence.

So we thought, How could they do this at work? What if we got people, on one day, to pay attention to girls in this way? As future employees, not for their bodies?

We thought it would just be a little day in New York [until] Gloria [Steinem] stopped by the foundation on her way to talk to Parade magazine, and we told her about "Take Our Daughters to Work Day," and then she told Parade, and that's how [the idea] got out into the world ahead of schedule.

Originally, the people at Ms. wanted a different day for sons, one which emphasized household work:

At this point I think companies that do it probably bring boys too. We hoped to do a Take Our Sons Home Day, and we wanted boys to learn about the house, what it’s like to be at home, and create a whole curriculum around the issue of two-career families. I think now companies talk to boys about how to be a father at work, but I still don’t think girls know all of the different jobs that are out there. They are not privileged to know what jobs there are in the world, and don't have the privilege of seeing what a big office looks like in the center of their cities.

As for its place today:

I don’t think there are as many people who need it because of the Internet. It's more accepted that women are there, working jobs, but it's not just for girls. Originally, we started it to remind adult women of what dreams they had. And there are still plenty of adult women who are not living out their dreams.