Light acts a wave (oversimplification... there is more, but I'll leave it out here).
When it is reflected from, or refracted through, two surfaces, two waves will be formed. When the resulting waves are in phase, it reinforces... the energy is combined; when it is reflected or refracted out of phase it cancels. What you see with "Newtons Rings" is actually caused by a very small varying thickness space; where the separation results in reflected light in phase, it is brighter; out of phase it is darker. The effect is "lines" indicating phase.
Note that the lines never cross ... that would require "in phase" and "out of phase" at the same time.
I hope that makes sense. I've done a lot of Interferometry ... and I understand the concept ... no trouble ... but explaining it in few words is tough.