Are you certain it's for eggs? I also see another identical piece in the background of the photo. I'm wondering if it isn't a device that is used to slice tomatoes uniformly. Place the tomato into the halves and slice in the slit openings. For example, check this item out. Just a guess.
I don't know what it would be used for. There are no cutting blades. It doesn't slice an egg or anything. My sister has never used it and doesn't remember who she got it from. She doesn't think it had any other pieces that go with it.