Assignments are a way to coordinate the movements of tribal forces.  When an assignment is made, a timer is set by the creator of the assignment.  Tribe members have this amount of time to join the assignment with at least 40 upkeep.  Once they have committed their troops to the assignment, their troops will be automatically marched to the destination in such a way that they all arrive at the same time.  Troops joining the assignment too late, or from a distance that cannot be covered in the time left on the timer will still be able to participate in the assignment but they will not arrive with the other troops.