When you are creating a New Class with the object type Assignment, an additional tab appears to the Class Properties dialog, the Assignment Details tab. It enables you to select the assignment type and certain conditions related to the completion or approval of the assignment.
There are two types of assignments, task assignments and approval assignments. The assignees of the task assignments simply mark the assigment complete when they have successfully carried out the task, whereas the assignees of approval assigments have more say in the actual approval process: they can use the assigment for approving or rejecting the target object.
In both cases, you can set the completion of the assignment to require action from all or any assignees. You may also want to require an Electronic Signature.