It's the Norden sight, and it's actually a combination of automatic pilot and ballistic computer. The Norden actually allowed the bombardier to take limited control of the plane (in the case of the B-17 at least, although variations of the sight were also used on the TBD Devastator and the B-24), program in the bomb type and factor in aircraft drift, ground speed and altitude to calculate a ballistic solution to drop the bomb load.
The sight had various setting knobs to "program" in altitude and weapon type, and gyroscope elements allowed the bombardier to input motion factors by optically tracking the target for a set period.
Now, that all sounds good and well, and the Norden was a pretty impressive piece of applied technology. But, we're also talking about dropping bombs from 20,000-plus feet, with all the inherent effects of winds along the bomb's path, storage damage to the bomb's fins, and in-flight damage to fins (part of the Manhattan Project's bomb casing development showed a pretty high failure rate of standard USAAF bomb fin assemblies).
And buffeting from flak, evasive action from attacking fighters and high altitude winds could also introduce solution errors or cause the bombardier to have to drop with an incomplete solution.
Also remember that the USAAF early in the war used the Norden to drop bombs on moving ships at Midway and during the defense of the Phillipines. That throws in a another variable that's awfully hard to if not impossible to account for, especially if the ship is not moving in a straight line.
The old "bomb in a pickle barrel from 20,000 feet" concept of the Norden is pretty far from reality. But you could still get a fair circle error of probability under some combat conditions or with a skilled bombardier. And in a lot of cases, USAAF bombing raids had a relatively more accurate targeting pattern than what you'd find with early RAF (pre Arthur Harris) Bomber Command planes and sights.
That's why USAAF heavies depended on box formations, interlocking fields of fire and escort fighters - to increase the odds of undisturbed bomb runs.
HTH