What does these colors don't run mean?

It means that they stand firm; they will not bleed or fade, they will always be the same colour, they won't back down, they won't change their mind, they will forever stay the same. For example , if a person tells you that his/her colors don't bleed, it means that he/she has taken a stand (an opinion or belief) and they will NEVER, EVER change their mind or back away from that decision. It means there is not one single drop of cowardice in holding and staying with the position they have taken.