A channel is a block of hardware (effectively a co-processor) which performs I/O operations, off-loading that work from the main CPU; they are connected to peripherals, and usually have direct access to main memory.
The details vary considerably from manufacturer to manufacturer: for instance, the Peripheral Processing Units of the CDC 6600 are effectively channels, but they are essentially complete minicomputers (although they are implemented with shared hardware).
For the channels which include a specialized control unit, not a full general-purpose CPU, the individual operations are called channel command words; they are generally stored in main memory, and are organized into channel programs.
IBM channels come in two varieties: a multiplexer channel handles a group of slow-speed devices, and interleaves operations to each of them, with each transfer handling single small data item (e.g. a byte); a selector channel handles high-speed devices such as disks and magnetic tape drives, and transfers an entire block at a time.
Channels were apparently first introduced with the IBM 709, and other manufacturers copied the idea.