The Zendikar block takes place on a plane where the world itself is a violent and unpredictable entity. Forests can spring up over night, and mountains can crumble on top of civilisations. Scattered around the world are mysterioius hedrons that, as it is revealed, are the building blocks of an ancient and powerful race called the Eldrazi. The Eldrazi were once contained by three planeswalkers, but were being released once more by the machinations of Nicol Bolas, for reasons unknown. The Eldrazi take calls from Cthulhu mythos, and are beasts from beyond mana, aligned to colorless, but not artifacts. All of them are amazingly expensive and amazingly powerful.
Zendikar - This set revolves around lands, and abandons the gold cards of previous sets, with every card being mono-colored. The set is large, with over 200 cards, rather than the smaller sets like Lorwyn. To promote the "adventure world" feel of the set, certain "priceless" cards were packaged, including some banned cards Wizards had claimed never to reprint. Zendikar's set keywords revolve around this setting. Ally is a new creature type, that triggers abilities when other allies enter play. Intimidate is basically Fear, only works with any color instead of just black. Landfall is an ability that triggers when a land is put into play. Quests are enchantments that gain counters as certain triggers are met, and when they reach a certain number of them, trigger a new ability. Finally, traps are spells that can be played for low cost or free if certain conditions are met. Zendikar's symbol is a hedron.
Worldwake - Zendikar's themes were continued in Worldwake, as the hedrons begin to activate, and the world prepares for the return of the Eldrazi. It includes more allies, traps, quests, landfall abilities, and so forth. It does include Multikicker, which is the old-school kicker ability, only you can pay it as many times as you want and trigger it's ability for every one. It includes the planeswalker Jace, the Mind Sculptor, the only planeswalker with four abilities. Worldwake's symbol is a hedron beginning to open.
Rise of the Eldrazi - Rise of the Eldrazi is the final awakening of the colorless god-beings, cards so powerful that merely the act of attacking causes the defender to sacrifice permanents. ROE introduced the Level Up mechanic, which small cards had a cost they could pay to become larger. Rebound spells are cast, then exiled, then are played for free the next turn and resolve into the graveyard. Totem Armor were auras that, when the attached creature died, bounced the creature back into play with only the aura sacrificed. Meanwhile the Eldrazi's signature, Annihilator, is a number of permanents that are sacrificed whenever that creature attacks. ROE's set symbol is a fully opened hedron.