Jump Drive Computers are part of the Jump Drive, the only faster-than-light way to travel, besides Warp Gates. Even though Warp Gates are better - they can move you 8 systems, whereas Jump Drives can only move you 8 sectors - they can't be built on Ships. This means that if you want to go from Point A to Point B quickly (on a ship), and there's no station where you're going or no station nearby, Jump Drives are the way to go.
Before using a Jump Drive, you must first connect the Jump Drive Computer to a Jump Drive Module. Then, you must charge it up. The more Jump Drive Modules you have, the faster it will charge. However, this charging processes does take energy from your ship, which means that if you want to constantly Jump, you should have plenty of Energy Reactors or Capacitors on your ship.