Daily Missions, AKA Dailies, are special missions that are available on the weekdays in a set sequence. They can be difficult, but very rewarding. Each comes in 3 difficulties - E (Easy), N (Normal), and H (Hard).
For the most part, the Monday and Thursday dailies are the most valuable.
Monday, AKA Golden Armor, is farmed for Gold and Platinum armors. Gold Armors can be discharged for 6k a piece, while Platinums are worth a ton of exp for your units. Golds are a fairly common drop, but Platinums are exceedingly rare until H, and even then it's only a 15% drop.
Being able to do this mission easily should be a first priority for all players. Note that H is much, much harder than N, and should be held off until you have multiple CCed units (~rank 50-60)
Thursday, or Guardian of the Magic Crystal, is your main source of Demon Crystals. Stock these up for use at the Trading Post.
More info here:
Daily Missions - Millennium War Aigis Wiki