Wealth: You fill in this bar by getting cash, stealing cars, taking control of businesses, buying houses, etc. The cash is straightforward. Your property, though, has to stay safe. Your garage full of stolen luxury cars, your six houses on the waterfront, the thirty bars and dry cleaners and shoe stores you've muscled into giving you a cut of the take - you've gotta keep it all intact to maintain your wealth.
Looks: You fill in this bar by stuffing your wardrobe with more and more expensive clothes; by visiting the gym to keep yourself in shape; by keeping your hairstyle up to date with the latest trends; by ferreting out private trunk shows by fashion designers; and by collecting accessories like cologne, cufflinks, gold necklaces, etc. Your looks have to stay current, though. Your clothes and hair have a decay rate as they fall out of fashion.
Infamy: You fill in this bar by committing crimes: killing, carjacking, bank robbing, all that GTA stuff. The more your Infamy fills up, the more recognizable you are on the street. You'll intimidate some enemies into surrendering on the spot, but others will make you a target just to make a name for themselves.
Influence: You fill in this bar by making deals with important people. Early on you're shepherding two gangs into joining forces to expand their joint territory. Later on you're getting a city councilman to cut a deal with the mafia. As your address book fills up with more and more powerful people, your Influence spreads. But those powerful people have powerful enemies who may come after you, and if your powerful friends end up dead, then so does your Influence.
I mentioned that each of these meters has thresholds every 20%. These meters are dynamic, shifting up and down depending on how the game is going. But whenever you get one to the next 20% threshold, that becomes the new floor for that meter. Get your Looks to 43% and it'll never drop below 40% again. This lets you experience the dynamism of the system without being forced into constant maintenance on everything all the time. You can push to get Infamy from 45% to 60% while coasting on Looks at 20%, then let Infamy sit at 60% while you get Looks to 40%.
Those thresholds are also used to unlock more content. In the case of Influence, I described how the kinds of important people you deal with changes over time. That's explicitly broken up by these tiers. When Looks crosses 20%, fashions change and now you need a new wardrobe, hair, etc., to get to 40%. When Infamy crosses 80%, random street punks no longer take potshots at you because you're too notorious - but skilled assassins start showing up to blow up your cars, set traps in your houses, and murder your Influence partners. So as you get each meter to a threshold, that aspect of the game changes and new content and challenges come your way.