The best way I can explain them is by saying Control Points are sort of like Masking, or making a Selection in Photoshop, if you're familiar with those techniques; but it's Masking/Selecting on steroids! And control points are sooooo much easier to do and so much more flexible. If NIK' has a Super Power, it's Control Points and if you're not using them you're missing out on probably half of what makes NIK' so amazing.
To try and explain what they do, Control Points "select" an area based on RGB values, saturation and brightness as well as location. You can adjust their size, move them around, use multiple points and group those multiple points. Once in a group, adjusting a slider for one Point communicates any changes made to every other point in that same group. They also "feather" edges of the selection automatically, so you get a smooth gradient automatically.
Watch this short video to get a much better understanding of what they are, and how they work:
Understanding Control Points. If you use NIK, you need to watch this video.
....