In the field of acting, a triple threat is someone who can sing, dance and act. A triple threat is so skilled that they can handle any part you throw at them; they're very good and very marketable. This is why actors are urged into acting classes, dance classes and voice lessons. But what would constitute a triple threat in the world of burlesque?
Looking at the strongest performers out there, I believe the burlesque triple threat has three components: choreography, costume and charisma. Choreography would include technique, musicality, skilled use of props and/or the stage. Costume would include the design and construction of the garments, their functionality and aesthetics, color and fabric choices. I'd probably put hair and makeup under costume since they integrate and complement one another. Charisma would include stage presence, confidence, characterization, personality and ability to win over an audience. I don't know that these have to be present in equal quantities to make a strong performer, but it gives us something of an equation to work with. Triple threat = C1 + C2 + C3.
Consider the award-winning performers you've seen and this equation. Award winners tend to have an abundance of at least two of the three components, if not all three. Consider your favorite performer at the latest show you attended. What was present: choreography, costume, charisma? What made this performer more appealing to you? I'm guessing it was some combination of the triple threat components more abundant than with the other performers in that show. Some performers have stronger choreography, some have incredible costumes, some have charisma for days (my 67 year-old father is incredibly charismatic). In the performances you don't like, what's missing? (I'm not naming names for examples of any of these C's; this is a rhetorical thing and a way for performers to up their games if they want. I'm sure you can find your own examples.)
How do you become a triple threat? Just like actors do. Last year I wanted to improve my costuming so I made Mega Costume and I'm consistently working to up my costume game. This year I wanted to become a stronger dancer (choreography) so I'm working on taking 100 dance classes and trying to incorporate more of the technique I learn into my numbers. I have some sliver of my dad's charisma, but I know I can work harder on connecting with my audience. Maybe one day I can confidently say I'm a triple threat as well.