Vices are negative leader traits. Part of the challenge of Saints and Sinners is overcoming your leader's Vices, and exploiting those of your rivals.
Aloof
Excuse me? Did you say something? I didn't think so. Your attitude has alienated you from the rest of the world, resulting in -50% political influence and -1 commerce per trade route. Not only are you vulnerable to the UN and the Apostolic Palace, rivals can use the Blamed Civic feature to drive up your maintenance costs.
Brutal
Your idea of empathy is free salt to go with those wounds. Invading a city leaves a trail of messy bodies behind. Where better to put them than in a Mass Grave (-2 Production, -1 Happiness)? Luckily, you can build Atrocity Museums to rewrite history with yourself as the victim of those vicious currs. Also, your populace never celebrates your rule with a 'We Love the King' day.
Extravagant
Why just one gold mine when you can have two? It takes 2 copies of any luxury resource for your greed to be satisfied. More than any other civilization this leaves you vulnerable to opportunistic pillaging and trade embargos designed to cut off your supply of fine goods.
Fatalistic
The sky is falling down! Your belief in everything paranormal leads your people to panic in 1 AD, 1000 AD, and 2000 AD. You also lose your cool if one of your cities falls to the enemy, or a nuclear strike lands on your head. Rival civilizations can exploit these weaknesses to great effect, so watch out when the nukes start flying!
Gluttonous
The best things in life are edible. Your uncontrolled eating depletes all cities of 1 food, taxing your start-up cities to find a good source of sustenance nearby or face starvation. Also, your flabby workers can only run half as far as your rivals.
Hawkish
For freedom! Or something. You've maintained power by promising to punish your rivals. Now your population requires you to make demands or go to war to avoid masses of unhappy mobs. You must also appease the populace by maintaining 1 military unit in a city for every 4 population points there.
Stubborn
Most people wouldn't walk into a hail of gunfire just to prove a point. But then, most people are not you. Anytime you are attacked by a unit with limited damage capacity your units take an extra 10% max damage before bothering to retreat. Be very wary of bombers and siege units, because they are coming after YOU!
Idealistic
Whoever said Idealism was a virtue wasn't a politician. Your moral reservations--whether real or feigned--prevent you from selecting any civic below tier 2 (though you are strangely willing to hold onto early civics until your grand ideas come to fruition.) In addition, you are unable to raze cities.
Libertine
Lead me not into temptation, unless of course you're hot. Your libidinous nature has led Hedonism to become rampant throughout your empire. It prevents religion from flowing naturally into your borders and results in -2 Espionage, -1 Gold per city. It also makes your rivals that much less likely to want to share Open Borders with you, as your lechery can spread.
Maverick
You've figured out the answer to the world's problems. Too bad the rest of the world doesn't agree. As soon as you or any rival has the technology to use your favorite civic, you are forced to switch to it. The populace rewards your cowboy shenanigans by rallying -25% less defense to protect your cities. You are thus vulnerable on two levels--inflexible in your policies, and an easy target for overrunning militarily, especially in newly founded or conquered cities.
Narcissistic
There's nothing you can think of that wouldn't look better without your face on it. Your narcissism means that any city without a statue of yours truly suffers -100 culture. And as the years press on, and you encounter bigger and more efficient ways to construct likenesses of yourself, expect your older statues to no longer satisfy your vanity. To make life the easiest for you, it's a good idea to track down marble, silver, gold, and other materials befitting of your statues. Just keep in mind the materials required become more exclusive as your ego grows.
Pampered
The world is a wonderful place as long as you view it through sculptured windows on a comfy couch with servants to attend to your every need. You suffer +25% war weariness and must gradually increase your spending on Culture, to the tune of 10% during the classical age and 20% during the Renaissance.
Paranoid
They're all out to get you! Your paranoia means you spend more and more on your espionage efforts, possibly at the expense of research or gold. You can not spend less than 10% on espionage during the Classical era, and not less than 20% after the Renaissance. In addition, any time a rival succeeds at a spy mission against you, your suspicions may lead you to eliminate one of your own spies.
Zealous
Onward Christian (or whatever) soldiers! Your appetite for the divine means your soldiers heal 10% slower when there's no missionaries around to validate their purpose in life. Also, once you choose a state religion, you're stuck with it forever. Be especially wary of multi-front attacks, because your clerics can't be everywhere at once.