There are two aspects to this statement.
First, why was so much owed to these people? This was because the people Churchill was referring to (the RAF) had prevented the invasion of Britain by Germany. If the Luftwaffe had succeeded in destroying the RAF and in doing more damage to England, Germany might have been able to invade. This would have devastated England. Therefore, many people were benefited by the battle.
Second, why were there "so few" who were owed? This is because the Battle of Britain was fought by a relatively small group of fighter pilots. They, along with the support staff who maintained the airplanes and used radar to direct them to the battles, were the only ones who really participated in the battle.