What does the quote Tigers die and leave their skins people die and leave their name means?

It's essentially just a reminder to be a good person, that your name is essentially your legacy, so be a good person so that it will be a good legacy. It does not mean name in the literal sense, it means reputation. As for tigers leaving their skins I am not sure, i think its about being memorable, because a tigers stripes are what make it distinctive, just as a persons character are what make them distinctive.