A decayed creature is a zombie token (or creature) that comes with a built-in drawback: it can't block, and when it attacks, you must sacrifice it at the end of combat. So you get one aggressive swing out of it before it dies. It's essentially a disposable attacker.
The most common mistake is thinking you choose whether to sacrifice it—you don't. If a decayed creature attacks, sacrificing it at end of combat is mandatory, regardless of whether it survived or dealt damage. Note that decayed only restricts blocking and forces the sacrifice on attack; a decayed creature can sit back and do nothing indefinitely if you never send it in.
In Commander, decayed tokens shine with sacrifice synergies and death triggers—their forced sacrifice fuels aristocrat strategies, Blood Artist effects, and reanimation. They also work well when you can remove the decayed counter or copy/blink them for value before they expire.