Part 2 introduces Davy Jones. Jack Sparrow has owed Davy a debt. Now Davy intends to make Jack make good on that debt. One way or another. Really awesome sequel.
I usually think that a good spell of time between an original and a sequel is a good thing. It gives everyone space to refresh the ideas and develop the characterisations. That's pretty much what Gore Verbinsky has done with this superior follow-up to the 2003 story. This time, we don't really need to spend much time on the who's who bits, so can head straight to the action which for the next 2½ hours follows "Jack Sparrow" (Johnny Depp) double-dealing as only he can try...