Barbossa was the captain who mutinied Captain Jack Sparrow and took his ship, the black pearl. He became cursed after stealing cursed aztec gold, and at the end of film 1, was killed by Jack Sparrow in revenge for the mutiny.
Tia Dalma, the voodoo lady from DMC, brought him back to life by her arts, as he knows the way/will help rescue Jack Sparrow from Davy Jones' locker. His appearance at the end of DMC is important because it signifies that Jack can and will be brought back to life, and that the pirates (who were once at odds with one another) will have to unite to fight a greater enemy (Beckett and the EITC).
Does that help?
I agree, it would be great to watch the first film again.