Answer:
The quote means that ego clouds the rational judgement of a person, acting like an anesthesia for the stupid things one have done, providing a short relief from any pain or embarrassment.
Step-by-step explanation:
The quote "Ego is the anesthesia that deadens the pain of stupidity" is a saying by Frank Leahy, an American sportsman and coach among others. This quote is meant to imply that people use their egos to hide the embarrassment or pain that they suffer.
For instance, fighting and quarreling about something that was so trivial but which was realized only later on. During the heated conversation, the issue may have also been understood to be insignificant but due to the ego of the persons involved, none was ready to let go. This ego clouds over the rational thinking, making the person reluctant to accept his fault and apologize. Thus, this short relief and contention with one's own acts acts as an anesthesia for the supposed "embarrassment" and pain a person's stupidity.