Plans are recipes that use different items in order to craft other things such as Parts, AirMechs, Pets and Variants in the Nanoforge. Some plans must be purchased in the Shop or dropped in-game before the item can be crafted. When you have a plan and own all of the items required to craft the item, just place the items in the Nanoforge and they will craft the specified item.
AirMech Plans allow you to construct an additional base type, which is required to unlock additional PvP and RPG loadout slots in the Hangar. Ownership of the plans is required in order to Nanoforge the AirMech.