Bruce lee did a lot in his life, and in the martial arts world he is a legend/hero/prophet.
He was the first famous action hero in his life time, and made action movies/martial arts cool. Bringing one of the first Chinese to introduce Chinese culture to America and the west in a mass market.
He used to preach that martial arts is for everyone no matter who you are, and many of his movies base around the underdog/neglected soul finding themselves in Martial Arts. He opened many schools and taught loads of people and many of his students even feature in his films. He didn't teach based on rigid practice but allowed people to go at their own pace, of course hard work was mandatory and you couldn't be lazy, but if it took you a while to perfect a kick it took you a while. it was no big deal.
Bruce Lee was a kind soul and often helped people with emotional problems, many of his quotes from his moives, speaches and books are still used and popular for martial artists and non martial artist. Many people find his philosophy on life to be a very good one. To sum it up he would say "Be water, and adjust to the situation, go with the flow." He was actually the first to write books on self-help.
Bruce lee also hated racism and back in his time, racism was huge in the west. His movies would deal with day to day problems any person if you were white, chinese or black for example would face. He made people appreciate their culture and not be afraid to stand up for themselves in the face of bigotry.
Bruce lee also had another philosophy and that was, DO. which meant that instead of saying don't or i cant, you DO it!. He had a fear of heights but would often free run to demonstrate his DO philosophy, where you cant be held down by your fears. So basically he is the father of free runners.
Bruce lee brought gyms to peoples homes, he would say that you don't need a fancy gym to work out and big muscles mean nothing, hense "I don't fear the man who knows 100 punches, i fear the man who knows 1 perfectly." Which means that you need to train your body and not have muscles.
Bruce lee was also very spiritual and the Wu Tang Clan often refer to Bruce as their prophet as he inspires them, how does the Wu Tang Clan relate to spirituality? Well they claim bruce lees speeches on spirutality were like the first form of free style rap. However, Bruce with his racisim would never hate anyone who wasn't the same religion as he was.
and Finally the biggest influence Bruce lee had influences in Marvel Comics, Stan Lee was a huge fan of Bruce's and would often be inspires to make characters/moves based off of him or his movies. There is actually a super hero dedicated to Bruce Lee but I dont think it is very popular.
That is why bruce is an inspiration to the world!