Common Meaning
Merriam-Webster dictionary defines the word allegation as a noun meaning the "act of alleging" and also "an unsupported assertion which has the implication of being unsupportable." Using the term "allegation" in a general statement implies that the speaker does not believe the person they are referring to is speaking the truth.
Legal Definition
The legal meaning of the word "allegation" is very similar to the common meaning, in that it describes a legal assertion (or statement) which must be proven to be factual. According to the Nolo's Plain English Law Dictionary, an allegation is a statement of facts believed to be true listed by a party in their pleading (or written complaint) which describes the party's position and what they intend to prove. These facts must be submitted in advance to the opposing party for their review. After this review, the opposing party has the ability to ask the court to reject the statement, if they can find reasonable (according to the law) objections to dispute the allegation.
Etymology
The use of the word "allegation" was first recorded in the 15th century according to the Merriam-Webster dictionary. Allegation is originally a French word which was derived from the Latin base word "allegationem." In the original Latin, "allegationem" was a noun implying one person interceding or making a representation on another's behalf. In both the French and Latin, the word had legal implications.
Synonyms
Synonyms are words which have similar meanings and can be used to express the same general meaning as another word. Synonyms for the word "allegation" include words such as accusation, avowal, charge, claim, declaration, plea, profession, and statement. Note that accusation, avowal, charge, claim, plea, and profession each have negative connotation that imply statements which have questionable validity.
Antonyms
Antonyms are words which have the opposite meaning of a specific word and can sometimes help you further understand the meaning of a word by expressing what the word does not mean. Allegation itself doesn't have specific a specific antonym, but the verb "alleged" (which is derived from allegation) has two antonyms: undeclared and unquestionable. These opposite words again point to the idea that an "allegation" or something which is "alleged" is considered an unverified and potentially false statement.