I mean, it doesn't really give the illusion of it. It is higher frame rate when recorded from a camera[1], as most TV was. The fields are independent moments in time (and you can very clearly see this in freeze-frames of interlaced motion, that's part of what combing is).
What it gives the illusion of is greater vertical resolution.
[1] video game systems that used interlacing, like the n64, playstation, and up until the hdmi era, did not usually do this afaik, opting to instead drop the frame rate to 30fps with 2 fields per frame, so they really were in many ways the worst of all worlds.