The side-cut is the curve on the sides of your snowboard. If extended it ends up forming a circle, that circle's radius, commonly referred to as "side-cut radius", (together with how much you bend your board while turning, the flex comes into play here) defines how large or how short the turns will be, the shape and size of your carved turns. Straighter side-cuts (bigger radius, until about 10meters) will make the turns larger, and deeper side-cuts (smaller radius, from about 6m) will make the turns shorter.
Various kinds of side-cuts:
Not every board has a side-cut equal from one tip to another and equal on both sides of the board (toes and heels).
1 radial side cut
2 progressive side cut
The typical one, brought from the ski industry along with the traditional camber profile, for decades it was the only one so it more than proved to work by now. A radial side-cut is part of a perfect circle. It feels like it always wants to make round turns, bigger or smaller, but rounder. With a radial side-cut it's harder to change directions during turns than with a progressive/multiple side-cut.
If the radial side-cut is part of a circle then a progressive side-cut could be part of an egg! The egg shaped edge makes the final part of your turns faster and more aggressive, while initiating the next turn gets easier (like the setback stance does). You'll find yourself accelerating in the end of and between turns, and maybe flying from one arc to the next. You get more performance out of your board with less effort.
Multiple / Combination side-cut
It can be multiple radius combined, or a radial side-cut combined with a progressive one (which in the end is just a type os progressive side-cut). The specific effect on riding will depend on the combination of side-cuts used, but it will somehow allow you to more easily change directions during turns than with a radial side-cut. They're usually used to make a board more dynamic and "all around". For example, a bigger radius (straighter side cut) at nose and tail combined with a smaller radius (rounder) at the center may give you large arcs with faster transitions and short turns.
Almost all boards are symmetrical, which means that the toe edge and the heel edge are equal.
But we don't ride 0º,0º degrees (your toes have more space between them than your heels) neither can we press the board equally on toe side and heel side, or have the same balance on heels that we have on toes. This is why heel turns tend to be harder than toe turns.
To help you overcome this natural physiological asymmetry the brands are making snowboards with asymmetrical side cuts, where the heel edge is smaller (the contact points are a bit closer from one another) and more pronounced (has a smaller side cut radius) than the toe edge. This will improve your balance and give you more control over your heel edge, making your movements come out more naturally and sharper.
Some rocker / hybrid snowboards have edge technologies that help them get the grip that the rocker base profile takes away. Some examples may be the magnetraction (libtech), under-bite / mid-bite (YES snowboards). The edge technologies are disruptions in the side-cut, making it a non continuous line.