A strong audition monologue should first feel appropriate for you—your age, type, personality, and the kinds of roles you could realistically be considered for. You want material that allows the people in the room to quickly imagine where you might fit into their production.
I also look for a piece with a clear objective and some kind of change or discovery. A good monologue gives an actor something to do, rather than simply providing an opportunity to demonstrate emotion. You should know who you’re speaking to, what you want from them, and why you need to say these words right now.
Finally, choose something you genuinely connect with and can perform confidently under pressure. An audition isn’t the time to prove how difficult your material is—it’s an opportunity to show the auditors who you are as an actor. The best monologue is usually the one that lets you walk into the room and immediately do your best work.