Today, no one uses dumb terminals or terminal emulators to connect to an individual computer. Instead, we use our modems to connect to an Internet service provider (ISP), and the ISP connects us into the Internet. The Internet lets us connect to any machine in the world (see How Web Servers and the Internet Work for details). Because of the relationship between your computer, the ISP and the Internet, it is no longer appropriate to send individual characters. Instead, your modem is routing TCP/IP packets between you and your ISP.
The standard technique for routing these packets through your modem is called the Point-to-Point Protocol (PPP). The basic idea is simple -- your computer's TCP/IP stack forms its TCP/IP datagrams normally, but then the datagrams are handed to the modem for transmission. The ISP receives each datagram and routes it appropriately onto the Internet. The same process occurs to get data from the ISP to your computer. See this page for additional information on PPP.
If you want to know more about modems, protocols, and especially if you wish to delve into things like PSK and QAM in more detail, check out the links on the next page!