The bindings are what connects you to your board and so their flexibility (along with the boots flexibility) will dictate how your body movements pass on to the snowboard. Just like the boards and boots, softer bindings are more used in freestyle for their tweak ability and harder bindings are more used in freeride because they offer the so needed support in big landings, hard carves, and fast powder slashes.Bindings Flexibility
Bindings Size (bindings x boots / bindings x board)
Bindings Discs (bindings x board)
There are 4 types of inserts used in snowboards to attach the bindings (4x4 standard inserts; 4x2 standard inserts; burton 3x3 inserts; burton EST channel system), 2 standard ones and 2 from burton only. All the brands make boards with 4x2 or with 4x4 inserts and burton makes boards with all the four types of inserts. Before burton invented their EST channel system and their 3D inserts all bindings came prepared to fit only 4x2 or 4x4 inserts. But because a big percentage of all the boards out there are burton snowboards, bindings brands have adapted and began to make bindings with discs that fit 3 or even all the 4 types of snowboard inserts. So it's not that easy to get some incompatibility nowadays, but keep an eye on it if you want be sure.