An allusion is never an outright or explicit designation of a person or anything that the speaker seems to have in mind.
The history book about America which Sam was reading made a brief allusion to the ancient Greek idea of what a democracy was.
Heidi made an allusion to her first marriage, but she said nothing more revealing about it.2. A play on words, a word-play, a pun (now considered obsolete): The editor of the dictionary was delighted to find out about a book of allusions with which he was unfamiliar.
3. A covert, implied, or indirect reference; a passing or incidental reference: The main thing to remember is that an allusion is a brief hint or a quick mention of something which the readers or listeners are expected to have some knowledge about.
4. Etymology: from Latin allusionem, allusio, "a playing with, a reference to"; from allus-, a stem of alludere, "to play, to joke, to jest."