Orders are powerful abilities that Welkin can use in Valkyria Chronicles, granting allies boosts in certain stats or doing things like evacuating an injured ally from the battlefield. These orders can be learned in various ways like ranking up units, or by talking to the Aged Gentleman in the War Cemetery.
Welkin issues the orders directly himself, and generally their effects will only last for one turn. Enemy commanders sometimes have their own orders that they can use against you as well.
Issuing orders during battle is very simple, while on map mode, the default view in battle, hit the triangle button to bring up a menu with all of your available orders. Keep in mind that orders do cost Command Points (CP) to issue, and better orders will generally cost more CP.