When a tumor is removed from a patient, it is usually send to the pathology the make sure that it has been excised completely to make sure there are no residues. Often this tumor is also used to analyze the mutation status of the tumor to determine, which further treatment is possible. For example, this is routinely done for melanoma where the mutation status excludes some drugs for further treatment.
Afterwards these tumors are important material for the scientific tumor research to isolate fresh cell lines or analyze them further. Parts of it are usually stored either frozen or as formalin fixed tissue to build tissue banks. These can be used for later research on this type of tumor and have a high value.
These tissues can then be cut and stained with antibodies or used for nucleic acid extraction (either DNA or RNA) or to test new ideas or methods which where not available to the time when the samples was archived.
Another famous case (although not from tumors) are tissues samples which have been archived from people deceased from the spanish flu in 1918, where parts of the virus was reconstructed using these samples decades later.