A video mode available on all VGA adapters, with a resolution of 320x200 with and 8-bit palette (or 256 colors at a time, available from 262,144 total color available from 64 shades each of red, green and blue). The "13h" comes from the fact that it is the 16th (or number 13 in hexadecimal) display mode listed in the BIOS documentation (see Int 10h), and the hexadecimal number 13 is commonly written as 13h in most x86 assemblers such as using Intel syntax, such as the Microsoft's Macro Assembler or MASM, Borland's Turbo Assembler or TASM, and Simon Tatham's Netwide Assembler or NASM.
Sometimes it is referred to simply as "Mode 13" because it was usually accessed through C or assembly language, where it would be implicity defined to be in hexadecimal, or through QBASIC, where it was accessed using the command SCREEN 13.
One of the reasons for its popularity was its extreme ease of use. It required a single interrupt call to enter (as opposed to all sorts of crazy register reads and writes to enter ModeX or the less-famous ModeQ). The video buffer began at 0xA0000 and ran for 64,000 bytes (so it could be accessed without switching segment registers), and each byte was a single pixel, making all graphical operations very easy (other modes had the bad habit of splitting the bits for pixels across several pixel planes, or using multiple bytes per pixel, or both). Changing the palette was a piece of cake, simply by reading and writing a few I/O ports on the system.