Flash Camcorders are camcorders which record video onto flash memory instead of a video tape. The flash memory can be a removable memory card (SDHC, Memory Stick, xD), or it can be built-in memory which is not removable. Some camcorders like the Canon HF S10 have both removable memory and built-in memory.
Removable memory is generally better in a flash camcorder because when you fill the memory, you can record more by inserting an empty memory card. Whereas with built-in you have to move the videos onto a computer before recording more video.
See related links for a list of flash camcorders.