Non-Abelian groups are mathematical structures in which the order of operations matters. In these groups, if you take two elements and combine them, the result can differ depending on the order in which you combine them. This is in contrast to Abelian groups, where the order does not affect the outcome. An example of a non-Abelian group is the group of rotations in three-dimensional space. In this group, rotating an object around one axis and then another can yield a different final orientation than if you had performed the rotations in the reverse order. Non-Abelian groups are important in various fields, including physics and cryptography.