Vox Populi adds some interesting game concepts, and some very involved mechanics to drive them, into the Civilization V game.
Here are just a few.
City-State Diplomacy[]
City-State Diplomacy is incorporated into Vox Populi that localize the influence of city-states preventing one civilization from buying out city-states for an alliance, but rather spend valuable resources for an alliance. In addition to localizing influence, new resolutions are added allowing civilizations to establish a permanent alliance or a sphere of influence on a city-state along with enacting a Cold War forcing tensions between the three competing ideologies!
Vassalage[]
Vassalage is a concept reintroduced in Vox Populi. Vassalage consists of which civilizations are signing onto an agreement to which they become asymmetric to each other. With this agreement, one civilization serves as the master in the relationship and collects tribute from the weaker, vassal nations. This agreement can happen voluntary or by force through capitulation. After reaching the Medieval Era, Vassalage becomes available in the Diplomacy menu.
Events[]
Warning: Vox Populi is balanced without the events. They can be disabled in the Advanced Setup panel.
Events are a feature reintroduced and expanded in Vox Populi. Just as in the real world, Events consists of a series of choices, which define the event's ideas and goals. In the game environment this is represented through a list of selections, which have a diverse set of possible effects. A well made choice may considerably enhance your civilization's abilities, although a bad choice may also do the opposite.
Monopolies and Corporations[]
Monopolies and Corporations are a new end-game concept introduced in Vox Populi. Monopolies take your excess resources to the next level of economic development when trading and resource advantage cease to improve your empire through happiness and yields and instead become a kind of economic system which installs empires with Corporations that can expand throughout other empires. Corporations can be founded by constructing a Headquarters. Each Headquarters requires a type of specific monopoly and corporations can expand in their founder's empire through the construction of corporate offices. Corporations can expand through other empires through corporate franchises which can appear after a trade route is completed between a city with a corporate office and a foreign city.
War Score and Unit Supply[]
War Score and Unit Supply changes how combat is simulated through reality as War Score will drive a nation's will to continue a war and Unit Supply determining the military strength of a nation while War Weariness being a major factor to both of these concepts.
New Units[]
There are new units in Vox Populi that changes the battlefield dramatically. The changes of the recon class and the addition of the new mounted ranged unit class shifts the balance of the battlefield as the recon class is now designed as a terrain specialist gaining experience through discovering new lands and receiving unique promotions that favors the vast terrain. The mounted ranged class combines the mobility and strength of the mounted units with ranged firepower from the ranged class making them become very favorable in hit-and-run tactics.
New Buildings and Wonders[]
New buildings are added in Vox Populi such as new religious buildings derived from additional beliefs added by Vox Populi or simple general buildings overall. The Well is an early general building that provides food and production bonuses, but can only be built in cities without a river. Watermills however are unlocked much later, but provide much more food and productions, while having the same requirement. National Wonders in Vox Populi no longer require the same building to be built in all cities, but rather rely on a national population requirement favoring neither tall nor wide playstyles. Reformation Wonders are also added to be constructed in Vox Populi as well by providing a reformation belief in the Holy City when their religion reaches a certain follower threshold.
New Improvements and Changes[]
In Vox Populi, civilizations may be granted new unique improvements or changes to their improvements that drastically change their play style. Kasbah, a unique improvement of the Moroccan civilization that used to improve desert tiles, now improves any tiles that surround a city while providing defensive bonuses and nearby attrition damage. However, general improvements are also changed as well. Farms grants an additional food for any two adjacent farm nearby while Great People Improvements now improves all luxury and strategic resources.
Happiness[]
The happiness system in the Vox Populi is completely revised, favoring neither tall nor wide playstyles. Happiness is now based on a cause-and-effect mechanism that makes your empire feel far more alive and dynamic than ever before.
Your happiness is displayed on the status line of the Main Screen (in the upper left-hand corner of the game). Watch it carefully. If it goes below 50%, your population is getting restless. If it starts to dip below 35%, you are in trouble. (Incidentally, you can get an excellent snapshot of your happiness by hovering your cursor over this number.)
One important note to remember - happiness generated from city buildings and city-based policies can never exceed its population.
Positive happiness increases the value of your national yields (e.g. your total science per turn), whereas unhappiness decreases them. You can see your current modifier by hovering over the 
icon in the Top Panel bar.