GW-BASIC was a version of the BasicLanguage available for early DOS machines. It came with the Dos Operating system.
GW-BASIC was named after Greg Whitten, an early MicroSoft employee. So says JoelOnSoftware at http://www.joelonsoftware.com/printerFriendly/articles/TwoStories.html. Other stories say that the GW stands for "Gates, William," "Gee Whiz," and other variants.
The original IBM PC had BASIC in ROM, supplied by Microsoft. It also came with PcDos and a more advanced form of Basic called BASICA, but that worked only if you had the BASIC in ROM. GwBasic was the generic MsDos equivalent for non-IBM computers, and would work on almost anything that was BIOS and video memory compatible.
Sample GW Basic code
Here's some sample GW-BASIC code, which reads a string, then prints it out: