The word obsolescence is the noun form of the more common obsolete, meaning "something no longer used." Both words stem from the Latin obsolēscere, which means, logically enough, "to fall into disuse."  The prefix "ob-" in obsolescere likely means "toward" or "against," and "solescere" is connected to "solere," meaning "to be accustomed".

According to the Oxford English Dictionary, the noun "obsolescence" was first used in English in the 1830s.  Specifically, the earliest evidence for its use in the OED is from 1832, in Noah Webster's dictionary.  The term is also closely related to the adjective "obsolescent," which appeared even earlier, around the mid-1700s. 

Examples of the word "obsolescence" used in a sentence: 
*"Once cell phones became equipped with visual tools, regular cameras became an obsolescence in the technological industry."
*"It was proven that the unused floppy disks were an obsolescence when they could not even be given away at a garage sale."
*"As I was cleaning out the office supply closet at work, I knew the shelf containing items of obsolescence like typewriter ribbon could be tossed out. "
*"Due to the obsolescence of the car’s transmission, the mechanic knew he couldn’t purchase the needed transmission from any manufacturer in the world."
*"Since the granite countertops were such an obsolescence in the neighborhood homes, the builder knew he would need to upgrade to higher quality materials like marble." 
*"The chief reason is not economic geography - the obsolescence of cities built to look to the sea or the coal fields."

obsolescence

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OBSOLESCENCE Definition & Meaning - Merriam-Webster

OBSOLESCENCE Synonyms: 21 Similar and Opposite Words | Merriam-Webster Thesaurus