The n-th braid group consist of all different ways n strings can be braided. The generators are all the over-crossings and under-crossings of neighbouring strings. They can be also imagined as world lines of n particles in 2 dimensions which changes its order.
The generators σi + 1 and σi − 1: And the transformation like:is not a braid.
The braid group plays key-role in the topological computing.