When your published missions receive response from your ambassadors (depending on your settings and type of mission), you may have to do some actions on your part to complete the mission. These actions can be found on the missions page under the mission dashboard, under the heading 'Missions that require action'.
There are three different actions you can take, depending on the mission you have published:
An ambassador can request to do your mission if you have applied this setting. This is most common with freebie missions, but you can change this to apply to any mission you like.
The number of requests a mission receives will fall under the 'Requests' column, and you need to go in and approve or reject these.
If a mission doesn't have automatic approval set, then you will need to approve or reject any mission submissions from your Ambassadors. These will appear under the 'Approvals' column, where you can go through submissions and reject any that don't fulfil mission requirements or are not worth the reward.
Anything that falls under the 'Awaiting Posts' column is to do with Ambassadors you have accepted to participate in a mission, who have not yet completed their task.
This is mostly to keep tabs on freebie missions and to see who is yet to complete their mission after being sent a product.