Drawing straws is a selection method used by a group to choose one person to do a task when no one has volunteered for it. The same practice could also be used to choose one of several volunteers should an agreement not be reached.
The group leader takes a number of straws or similar long cylindrical objects, and makes sure one of them is physically shorter than the rest. He then grabs all the straws in his fist such that all of them appear to be of the same length.
The leader then offers the clenched fist to the group. Each member of the group draws a straw from the fist. At the end of the offering, the person with the shortest straw is the one who must do the task.
This practice is immortalized in the cliché "drawing the short straw," meaning to be randomly, unluckily, or unfairly selected to perform a task or suffer some penalty.
*definition from wikipedia.