The prosecution history of a patent or patent application is (ideally) a complete record of the proceedings before the Patent Office. It includes any remarks or representations that have been made by the applicant concerning the proper interpretation of the claims.
Claims must be interpreted the same way in litigation as they were in the Patent Office, otherwise applicants could treat their claims as a "nose of wax" -- to be twisted one way to avoid the prior art, and to be later twisted another way to encompass an accused product as infringing the patent. This would hinder potential competitors who should be entitled to rely on the public record in judging the scope of the patentee's claims.
Claims must be interpreted the same way in litigation as they were in the Patent Office, otherwise applicants could treat their claims as a "nose of wax" -- to be twisted one way to avoid the prior art, and to be later twisted another way to encompass an accused product as infringing the patent. This would hinder potential competitors who should be entitled to rely on the public record in judging the scope of the patentee's claims.