This is a pretty simple question... What are missions?

Missions are errand quests for pets.
You can find them in the barracks in town.
Here you can see Sheryff Thyrm explain missions:



For example, I've chosen the easiest mission "Transporting Supplies" underlined in Red. Required level is 0, but Florian here is level 60, well over the level cap for this mission. Difficulty is Easy. Emphasized Statistic is Dexterity, meaning you want a pet with high dexterity to go on the mission. Duration shows how long the Sylesti will be on the mission, this example shows that it is one hour.




The Objective gives a short description of the mission and the reward for completing the mission is listed below the objective. This mission upon a successful completion will reward 200gold, 10 reputation points and a lesser mission satchel.

Mission satchel's can contain a variety of items: Gold, equipment, essences and potions/elixirs.
They're primarily used at higher levels as a way of obtaining a good amount of gold as well as healing items~
It's good to start when you're at a lower level too though as missions also give experience and help level up pets. :)

Well, Eim beat me to it and explained it really well but my guide might also be of service ^_^

sorry to just burst in but... hi Hundy! :-)