Order theory deals with properties of orders, usually partial orders or quasi orders but not only those. Questions about properties of orders, general or particular, may fit into this category, as well as questions about properties of subsets and elements of an ordered set. Order theory is not about the order of a group nor the order of an element of a group or other algebraic structures.
Order theory is a branch of mathematics which investigates the properties and structure of partial orders and quasi-orders (or preorders).
These sort of orders appear naturally in the mathematical universe; such as the $\subseteq$ relation, or $\leq$ on the integers. It follows that these orders (and quasi-orders) appear in our lives as well, e.g. "which item is more expensive?"
Some mathematical concepts related to order theory are: