Instead of having an internet account for each PC, you have one internet account and all the PCs in the network use that account to access the internet. Many families with children have more than one computer. One for the kids to play games and surf the net and one for the parents to do word processing, financial stuff and internet access. People with one computer often get a second phone line just for internet access if they use the net allot. With more than one computer in the house, there are bound to be conflicts over the use of the phone line.
Home offices can also have more than one user.
Internet connection sharing is a cost effective way of letting everyone in the office and home have access to the internet at the same time if needed. If you're a student, then you know that households of three or more students, all with their own computers, are not uncommon. If everyone wants their own access to the internet, it would require a phone lines and internet accounts for each person. By networking all the computers together and using internet connection sharing, only one line and one net account is needed. For internet connection sharing to work, all the computers that want to access the internet have to be networked together.