For the performance itself, the San Diego-based company AV Concepts used an updated version of the stage technique "Pepper's Ghost," which was first invented by John Henry Pepper for an 1862 Charles Dickens theatrical show. In essence, the illusion uses the fact that glass can be both transparent and reflective to create effects that confuse the two. Perhaps the simplest way to understand it is to think about your living room windows at night. If you have your indoor lights on, people can see in but you can't really see out -- the light reflects back at you. If you turn off the lights inside, the opposite happens and people can't see you from the street.
The same effect is in play with Pepper's Ghost: Trickery with your light source makes objects reflected in a glass look like they're on the other side of it. The area where the image appears is built to be identical to the hidden area where the object actually is, so the glass we're looking at is actually doing double-duty: Both reflecting the hidden area (the "blue room," in theatrical parlance) and transparently revealing the area we're supposed to be looking at. The illuminated objects in the hidden area, then, appear to hang in the room we're actually looking at.
For the Tupac illusion, for example, the video was actually projected from above the stage, straight down onto a reflective surface that bounced the image up onto a Mylar screen for Snoop to sing along with. Because the only light source being reflected onto the screen was Tupac himself, the stage area and the mirror that bounced the image onto the stage foil looked exactly the same, letting Tupac's image hang in the air ... just like a ghost.