Your Daily and Alliance missions are a source of experience for your commander, resources, loyalty funds and mods. While the missions are usually basic or standard and give you negligible amounts of each, there are higher level missions like "elite" and "legendary" that can give you substantial rewards. A legendary mission can produce well over a million XP for your commander, helping him to level up and gain critical skill points. Daily and Alliance chances will give you a full refresh of your missions, giving you a chance to get better quality ones. But you can still complete the missions given to you initially, you don't need to swap them, so complete them all and then use your chance to get a whole new list of missions, possibly containing a higher level one.
Missions are a great way to level up your commander, so if you have spare gold, consider purchasing chances. Better yet, ask you Alliance to put them in the alliance store so you can use your loyalty funds to buy them.
