Plasmas work by exciting phosphors like a CRT; the mechanism is different is all. Over time those phosphors wear out, just like a CRT. Newer plasmas have better phosphors and electronic trickery to skirt the issue a bit.

LCDs wear out, too, but that's from the crystals wearing out and becoming unable to flip states. That shows up as a persistent image that doesn't go away. Plasmas also have image persistence that looks like burn-in, but goes away after a few moments.