Early Access is a relatively new way of crowd funding similar to kickstarter projects, the main difference is that you get a playable yet unfinished product for supporting the developers by paying a moderate sum for being able to play a game as it is being developed. It's like you paid for a preorder, but instead of waiting for the game's release, you can already access some of it's features. The main requirement is that the game is PLAYABLE in its current state. In other words, this is neither alpha nor beta testing. You're buying a game that's not yet finished, yet you can play it since it has available some of the aspects promised for the full version. In other words it's like you've paid to play a very big demo.
Why is it popular?
Early Access (often referred to as EA) has become very popular on Steam, since the platform allows updating a game with ease. This way you can have the game auto update itself whenever a new patch comes out. The main aspect of launching an EA project is the hype that comes with it. It usually has a giant fanbase from the beginning, and the ideas that are presented make hundreds of thousands of people pay for the Early Access to a game that they've been promised. This way, the publishing company receives funds to make the game better - add new features, polish the graphics, introduce new content and of course make it possible for more players to enjoy.
The controversy with Early Access games
For a long time, the game developers have been trying to find new ways of selling their product for more money, mostly by squeezing extra payments out of existing titles. The thing about the game development is that it became easy for big and rich companies which overplayed the DLC system, for example. While a long time ago you'd receive a full game and some time later you'd have a DLC available that was almost like a second part of the same game, nowadays you're mostly getting content that was cut out of the original game before release, so that it could be sold for extra money, for example.
Another overplayed system was the Free to Play type of games where you could download a game for free and enjoy it, but the paying customers would get extra features that made the game easier for them or lifted some limits. A lot of companies have made their games pretty much clones of other titles and mooched off of players getting frustrated with not getting what they wanted for free, so they'd spend real money on them. Soon the term "free to play" got a rather negative reputation, partially because of its ways of trying to make players play their title daily (for example you'd get some reward if you did some mundane activity every day for a week).
Like the aforementioned systems, the EA concept gives a lot of opportunities for ruining its repute. For example, if a title promises new features and steady updates, but doesn't deliver them for months, or even years. They got the funds but decided to spend them on other stuff instead, and so the updates come at a very slow pace, or pretty much stop. Another thing is, even though EA titles require to be playable, the publishers have very different definitions of what playable means. For example, if there are several game breaking glitches that allow exploiting a PVP game, it's pretty much unplayable until it gets repaired. But what if the glitches stay for months, and cheaters are able to, for example, destroy enemy bases when they are offline, with simple tricks? That's one of the flaws of the early access games - there's a lot of glitches that make the game unbalanced and prone for having your multiplayer experience ruined, even if the game is getting patched regularly. There's also the thing about the community having a lot of impact on the game. For Early access products there's also a bit of an issue with adding what the community wants, and some requests are down right ridiculous. Unlike with a complete and coherent system devised by the company and released on the day of its premiere, an EA title might find people complaining about something not being present, or about a system that doesn't work very well for them. This way there's a lot of negativity towards some of the more challenging features, and they might get dumbed down, so that the negative Nancies stop complaining about it.
Should you risk buying an Early Access title?
That's entirely up to whether you feel like you can enjoy it in its unfinished form. As with every game bought on Steam, you have two weeks to get a refund, unless you played that title more then 2 hours total. It gives you enough time to figure out whether or not it's worth investing in the unfinished product you're funding this way. A pretty solid approach would be to treat it like a preorder so that you don't get disappointed, and if you learn that the game you bought won't likely become what you imagined it to be - return it. You can pretty much buy it later when it's out as the full version, although you'd likely have to pay more than what it cost in Early Access. If you decide that you don't want to play it in its current state, you can also pay for Early Access but wait until it's out as a full release, since you already bought the game and don't need to pay for the full version later even if it's more expensive than it was while unfinished.