An extinction procedure is essentially an intervention that makes a behavior occur less often or stop occurring altogether.

   Extinction procedures apply the "principle of extinction" which proposes that because behaviors occur for a reason - they get us things we want - if we stop getting what we want after we engage in a certain behavior then that behavior will eventually stop occurring because it no longer serves any purpose for us.

   Said another way, any behavior we engage in will become "extinct" (stop occurring) if it no longer has a function.

   Applying the principle of extinction to implement an extinction procedure means that you would deliberately stop allowing a behavior - a “target behavior” - to obtain the reinforcing outcome(s) that the behavior has always previously gotten. This procedure then makes the behavior ineffective and so it will occur less and less until it eventually stops altogether.

   You could describe it as a procedure where you would stop giving the behavior “what it wants” and what it has always gotten in the past.