I'm not talking about digging up dirt or finding out things that you don't actually have a right to know. I'm referring to current events that affect your employer, or things they've done that are in the news. Additionally, this could encompass the organization's history or initiatives and partnerships that they're currently involved with.
There are quite a few ways that you can learn these things. Most companies have internal websites where news and other information about the company is posted, in addition to what is available on their external sites. Additionally, you can search for the organization's name in Google News or another news aggregator website to find articles, pictures, and video involving the company and their activities. You can also do this to find information on competitors, the industry as a whole, and trends that may affect them. And of course, there are the social media platforms that companies are increasingly taking advantage of, like Facebook and Twitter. Odds are good that your company has some kind of presence there by now (and if not, it needs one, yesterday).
Why keep track of all this? Well, for one, it can help you do your job better. For example, I've been able to learn about flooding shutting down a facility before the official communication from the company was received. Another example are the multiple times I've found about about problems with products before official recalls were issued, allowing me and my coworkers to brace ourselves for the increased workload. But another reason is that it makes others see you as a resource and someone who knows what's what with the business, and someone who is capable of thinking strategically and using new information to good effect. It will impress those you work with and those you work for if you know what's going on.
I'm sure there are ways of learning about a company, organization, or industry that I would never even think of on my own. They don't call it the Information Age for nothing -- with more ways to learn and keep tabs on the world than ever before, there's no excuse to not be informed.