It is a general pick up point for the post office used in neighborhoods. As long as the right amount of postage(stamps) is used any letter can be put in it. They are usually serviced once a day and the time is posted on the box that the postman will be there approximately to take the mail out of the box. If you did not have the boxes you would either have to leave your mail in the mailbox at your house/apartment and the mailman would pick it up there on his rounds. If you needed it mailed sooner you would have to take it to a a main branch office of the postal service.
Different countries, USA excluded, have different color postboxes for different reasons. In Germany yellow boxes are for Deutsche Post while blue are for private carriers. In other countries, again USA excluded, different colors stand for the type of mail: First-class, second-class etc.