The word "allegation" comes from Latin allegatio ("a sending, dispatching"). stemming from allegare ("to send for, to send on a mission, bring forth, produce in evidence"), combining ad- ("to") and legare ("to send as a representative, depute").  It entered English via Old French (alegacion) and Middle English (allegen).  While originally about bringing someone or something forward in a formal court (like a representative), its meaning shifted to the act of formally stating something, often with the implication that proof is lacking. 

According to the Oxford English Dictionary (OED), the noun allegation first appeared in English during the Middle English Period (1150-1500), with the earliest known evidence dating back to 1402.  It came from French and Latin, building on the verb 'allege' (around 1300) and evolving into related forms like 'alleged' (c. 1425) and 'allegedly' (1823). 

Examples of "allegation" used in a sentence: 
"The police are investigating allegations that the mayor has accepted bribes." 
"The mayor denies the allegations (that have been made) against him."
"There have been allegations of fraud in the city government."
"I hope you have proof, because you're making a serious allegation." 
"I have received a letter accusing me of not clearing up after my dog, I wish to refute the allegation." 
"They were probably responsible for the allegation, made by a Carmelite, called Latemar, that John was conspiring against his nephew." 
"According to Bale and Foxe her husband turned her out of doors, but in the privy council register she is said to have "refused Kyme to be her husband without any honest allegation." 

I have noticed that traditional media outlets are almost overusing 'allegation' and alleged when reporting on someone's criminal behaviour, all the way up to a guilty verdict in court. Obviously this is to avoid possibly being sued if the court verdict is 'not guilty'.