Network booting, or booting from LAN as it is also called, is a process which allows a computer to start up and load an operating system or other program directly from the network without any locally attached storage device, like a floppy, CDROM, USB stick or hard drive.
On Intel architecture computers this is made possible with the PXE standard. PXE extends the features of the BIOS so that it can run software directly from the network. PXE support is now so common that you can expect it to be present in any reasonably modern computer that comes with an Ethernet jack (commonly known as RJ45).
This fact alone makes it possible to boot an Intel-based computer from the network without having to burn an EEPROM on your network card, like you had to do in the past.