In the past, U.S. Citizenship and Immigration Services (USCIS) required only that applicants up to age 75 provide fingerprints (also called "biometrics") as part of applying for naturalized U.S. citizenship. The reason was, apparently, that obtaining a clear set of prints from someone of advanced age was difficult, and could lead to errors.
But the technology has been improved and updated since the original policy went into effect. Now, says USCIS in an announcement issued July 26, 2017, the agency is confident enough in the new technology that it will immediately begin requiring applicants of all ages to comply with the biometrics requirement when applying for naturalization.
(For now, at least, USCIS is not extending this requirement to any other sorts of applications for immigration benefits, such as green cards or asylum.)
The new requirement has already been incorporated into Chapter 2 of the USCIS Policy Manual. Nevertheless, the agency will be accepting public comments on this matter, so there is a chance that further changes or amendments could be made.
In the meantime, if you are applying for naturalized citizenship, you can expect to have your fingerprints taken. This is ordinarily done by USCIS, at a facility called an Application Support Center or ASC (hopefully near where you live). (See "Where Do I Get Photos and Fingerprints Taken for My N-400 Citizenship Application?")
If you have some physical issue or disability that makes it difficult for you to provide fingerprints, USCIS should be willing to make special accommodations for you; and if all else fails, to waive (overlook) the fingerprint requirement entirely.