Daily Missions are special missions that are given in the game every day of time in real life.
They are outside of the campaign. You can use the same soldiers you use for other battles and they will get exp too. After each mission you get a reward that is usually good and there is 10% more chance for custom weapon. It is like in the campaign where you get golden mark. Enemies in these missions are randomized and they have random names. These missions are very long unlike in the campaign and usually require a high amount of points to complete.
If the daily mission is Capture the Flag mode, you will get instant victory before the battle starts (but teams will have 0 kills and you don't get exp, but you get rewards. This bug is already fixed in the latest version.