Ultra DMA (DMA having already defined above...) is a term used exclusively to describe IDE controllers.

The Ultra means that the controller can interface with the drive using Ultra ATA, which is a double-pumped version of original ATA. While the clockspeed stays the same, the Ultra ATA protocol transfers data on both the rising and falling edge of the clock pulse, leading to twice the throughput of original DMA.

This doubled speed is already reflected in the numbers (so a UDMA 66 bus, for instance, actually runs at 33MHz), making the 'Ultra' a bit of a marketing term.