I played the Beta, so things might have changed in the meantime.
The game can be divided into two parts: several series of scenarios, which are for either 1, 2 or 4 players, and PvP (ie. Skirmish), again with varying team sizes (but usually 1v1). Once you beat a scenario on standard difficulty, you can play it again on a higher difficulty - there are 3 difficulty levels, but some scenarios don't have versions in the Standard difficulty. Rewards for completing a scenario are gold and "upgrade cards", which can be used in combination with the real version of said card and some gold to give a minor improvement to the card. There's only one way of advancement, so don't expect RPG elements here.
The card mechanic is well executed - cards are divided into creatures, buildings and spells, and in four schools of magic. Balance is achieved via "orbs" - to cast a card in game, you must have the appropriate number of orbs in the right school (also, some cards require for example 4 fire orbs, while some require 1 fire orb and 3 "anything" orbs, which allows for improved combining possibilities between two schools of magic). IIRC, there was over 200 cards and they are planning to implement more (obviously some are rarer than others, I believe the basic cards already amount to 80 or so).
Once you get into the game, gameplay is fairly standard (which is not a complaint). Other than orbs, you need power to use your cards, which regenerates over time (basically, you've got a "graveyard" pool of used power, it's filled when a summoned creature dies or as soon as a spell is cast, and that power will slowly convert back into usable power). There's a fair amount of units, with varying abilities, balance is alright, there's a strategy element ("should I cast a spell here, or summon more troops over there"). Scenarios are interesting, the odds are usually stacked against you. The group scenarios are interesting too, though they usually boil down to everyone being cleanly divided and it playing like a SP scenarios, with the caveat that if one of the players is doing badly, everyone gets screwed. <grin> Of note is that the network code was apparently quite bad, as my 2mbit/s connection lagged terribly with 4 players (and apparently there was a 12 player scenario too!).
In the end, the game is still mostly about building the best deck, and the game doesn't really disappoint in this regard. There's a simple way of pitting units against each other and testing everything out (sadly, only those units you own), so those who enjoy this will like it. As I gathered, the main criticism was aimed at the price of booster packs or somesuch.
All that said, though, I've no plans to buy the game.
EDIT: And yes, everything is online, you have to connect to their server, even if you want to play on your own.