DMA, or "direct memory access" is found in a number of computer systems, not just the Super Nintendo. It’s basically a way for a peripheral or coprocessor to read data directly from memory, instead of requiring the main CPU to do a number of reads and writes. This is typically faster, if only because it lets the system skip the opcode fetch-and-decode. In the SNES, the CPU is paused during DMA since the address busses are in use for the transfer.
HDMA is similar in concept, though rather different in execution: instead of transferring a block of memory all at once, it transfers a few bytes during the H-Blank period of each scanline. This is extremely helpful, as most PPU registers may only be changed during a frame (at least without glitching) during this narrow window.
The SNES has 8 channels (numbered 0-7) that can be used for either DMA or HDMA