Android's open nature means that applications can be distributed through various outlets apart from the Play Store. Hackers love opportunities like these, because it means they can take existing applications and add malware of their own, or build an app of their own to ensnare downloaders.
Malware on Android definitely exists, though it isn't extremely widespread. Granted, it is more common than malware on iOS seems to be, but for the most part you're unlikely to download anything malicious.
Google are trying to keep it that way. To do so, they're changing policies. This policy change includes new rules on app naming, a ban on apps which do not clarify when information is being shared, and more detail on payment.
More rules on app naming is not a bad thing, since it is intended to cut down on copycat applications entering the market. If you remember Temple Run's exclusivity on iOS, a false Android app reached the market before the real Android port of the game. While not malicious, it was still frustrating for fans to discover it was a waste of time. All it did was show a countdown to the release of the real thing. It might be the first time someone has shared an application only to disappoint.
Apps which introduce vulnerabilities to the device are not permitted any longer. This should hopefully not effect apps requiring superuser access (also known as root access), since the Play Store has always allowed them to be hosted in the past. More than likely, this is targeted towards fairly obscure apps which can introduce issues in certain phones.
Push button, waste data. Not anymore thanks to policy changes.
There's another change, and this one really should put a smile on your face. AirPush is no longer allowed, falling under the 'intrusive advertising' banner. The ad provider would push ads to your device's notifications and basically devour data. Maybe not a problem for those with unlimited data, but now it's not a problem for anyone.
It's all very reasonable, really. You want the best for your Android phone, and they want to ensure you get the best from it. That means not downloading dodgy little apps you don't recognise, and sticking to the main forms of distribution is the way to do that.