While playing Borderlands 2, you'll have the chance to complete various challenges (or they will just happen as you play) and you can keep track of them through the menus. For completing each rank of a challenge, you'll collect badass points (1, 5, 10, 50, 100 points for each of the five ranks). When you hit certain Badass Rank thresholds, you'll acquire Badass Points. Each Badass point can be used to increase things like accuracy, maximum health and other innate abilities.
The interesting thing about Badass Points is that they are attached to your profile and not your character. When you use a point to buy an upgrade, that upgrade will appear on every character whether they be older or not yet created. Similarly, any points you have that are unspent, will be accessible from your other characters so that they may be spent.
The challenges that a character goes through to collect Badass Points are actually character specific though so while you are no capable of redoing the challenges on a particular character, every character can do every challenge and increase your Badass Rank further (which DOES transfer). In this way, your Badass rank, the number of points you can get and the upgrades you can buy are theoretically infinite and have no cap.
