The Hamburg Passenger Lists were created when passenger ships left the Hamburg harbor. Depending on the year, they contain different levels of detail about the individual passengers.
There are several resources to help you find your ancestors, if they chose to leave through Hamburg. The detailed explanation what is contained in these lists and how to find it, is listed in this PDF. A shorter online version is available on FamilySearch Wiki.
Images of the original lists are accessible on FamilySearch free of charge. These images are not searchable through an online search-box. Please use the digitized Klüber card file to find these ancestors (for explanation of the Klüber card file and its coverage please see the above mentioned PDF file, pages 2-4).
Ancestry.com also offers the Hamburg Passenger Lists, but only accessible behind a paywall. Please be aware that the indexed names are sometimes inaccurate because some names were hard to decipher. Therefore try different spelling variations when searching those.