Rank is the way to measure the fighting experience of a character. Older characters will have a colored ring around their base, and characters from the Avengers set forward will have this on their character card as a colored background to the character's picture in the upper left corner.
There are three colors:
Yellow is the Rookie version of the character, signifying the least experience.
Blue is the Experienced version of the character, signifying the character has a couple of years or been through very dangerous situations and knows how to control their powers and fighting ability
Red is the Veteran version of the character, signifying the character is at the top of their game. These are often the strongest versions of the character in the set.