What does "mailing software" do?
First it reads all the addresses in your database and matches them to the USPS database ultimately providing you a form called a CASS Statement the USPS wants. If an address doesn't match, the address cannot be included in a discount rate mailing. You can edit those bad addresses later. Next, the software sorts all the good addresses in the order the USPS wants them, starting from the first piece of the first tray to the last piece in the last tray. There is no manual sorting to be done - just keep them in order when printed!
The software will generate the tray tags in order, prepare a listing of the sort itself and then prepare the form the USPS wants for charging postage (3602, etc) which also tells you how much to bring to the PO.
Obviously this is a simplified version meant to convey a basic description of what mailing software does. It's primary purpose to you as a mailer is to save postage but the time saved in preparing a mailing versus the old way is also very significant.