A drum is a large metal cylinder that is coated on the outside surface with a ferromagnetic recording material. It is, simply put, a hard disk platter in the form of a drum rather than a flat disk. A row of read-write heads runs along the long axis of the drum, one for each track.
This is a key difference between a drum and a disk, with a drum the heads do not have to move, or seek, in order to find the track they are looking for. This means that the time to read (or write) any particular piece of data is smaller than it would be on a disk, the controller simply waits for the data to appear under the proper head as the drum turns. The performance of the drum is defined almost entirely by the rotational speed, whereas in a disk both rotational speed and head movement rates are important.
Performance was still an issue however, and programmers often took to hand-writing the code onto the drum in a particular fashion in order to reduce the amount of time needed to find the next instruction. They did this by carefully timing how long it would take for a particular instruction to run and the computer ready itself to read the next instruction, and then placing that instruction on the drum so that it was just arriving under the heads at that point in time.