The noun discrepancy is from Latin discrepantia, from discrepare ‘be discordant’ or 'to sound differently', from dis- ‘apart, away’ + crepare ‘to rattle, to creak’.  

The first known use of the word "discrepancy" in English dates back to the Middle English period, in the late 16th century, specifically in 1579 in the writing of T. Pritchard, according to the OED.  Discrepancy means an "unexpected difference," especially in to amounts or two sets of facts or conditions, which suggests that something is wrong and has to be explained. 

Examples of "discrepancy" and "discrepancies" (plural) in a sentence: 
"There were discrepancies between their accounts of the accident."
"Discrepancies in the firm's financial statements led to an investigation."
"A federal investigation showed huge discrepancies between names on the list and the existence of valid social security numbers." 
"Very recently in a business of mine we noticed cash discrepancies, and conducted an unannounced check at the branch concerned." 
"The photographer has noticed an amusing discrepancy between his glorious appearance and its inglorious origins."  
"A federal investigation showed huge discrepancies between names on the list and the existence of valid social security numbers." 
"Very recently in a business of mine we noticed cash discrepancies, and conducted an unannounced check at the branch concerned." 
"It is one way of addressing the huge discrepancies you can get." 

Just the facts:

DISCREPANCY Definition & Meaning - Merriam-Webster