What is the purpose of the 4-digit number after the 5-digit zip code and how is it determine?

This is to divide the zip code into smaller areas too. With subdivision growth in many rural areas, even not so rural areas, they needed a way to speed up the delivery even more. It's a subset of the 5 digit code.

It should help the carrier divide up his/her route better and carry only the mail for his/her subset. Helps in the sorting process.

This is called the "Plus 4." It is used for sorting mail into sector segments. Each block or side of a block has a different number, so your "ZIP+4" tells the Postal Service exactly which block you live in. This is used by major mailers to get the mail further presorted before they mail it, allowing them further discounts. Our machines also "look up" the ZIP+4 for each address that doesn't have it in order to spray a barcode that has that number and the last two digits of your house number on it. So, the barcode on the bottom of your mail is yours uniquely! The machines at the postal plant use this barcode to actually sort the mail in delivery order for each carrier (called Delivery Point Sequencing or DPS). So about 80% of the mail we receive is already trayed up and ready to go to the street for delivery without anyone having to sort it by hand. This does speed up delivery and allows us to use less carrier to deliver more mail since they don't have to spend the extra time to sort the mail before delivery. Our machines can even read handwriting and convert the address to the proper ZIP+4 and barcode. Neat!

It's just a sub-zone within the zip area just more specific. Using it can sometimes shave a day off of delivery as it skips a step in the sorting process.