The simplest way to describe it is protecting your good name in a world where a photo or blog post can circle the globe at the speed of light.
I sum it up as a formula, derived via google: Do a Google search for your name or brand. Look at the first three pages of results. How many of those refer to you? Of the ones that refer to you, how many do you control or have influence over. If this number is a ratio higher that 3:1 then you're in good shape. Example: 30 results, 20 about your brand, 18 are pages directly stemming from your efforts (your website, your sister-sites, your press-releases on other sites, etc).
Google results are an easy check, but at the end of the day, I use two things to manage my personal brand, and the same two tools work equally well for a corporate brand. The first is Google Alerts. This service scans news, blogs, and the web and any mention of your keywords and trigger either an 'on-the-fly' email with the story, or a digest, sent daily, with all the stories. If you're monitoring a very popular keyword or well known brand, the digest is the better choice.
For real-time monitoring of what's being said, I go back to Twitter. Twitter represents what is being said RIGHT NOW on the web. Using a tool to track your keyword in real-tinme on Twitter will tell you what people are saying. I use Monitter, because I like the multi-pane approach, and it lets me see the speed of the conversation too.
At the end of the day, there is more to Brand Reputation Management that just knowing about the conversation-- you have to act on it. participating in Twitter is the easiest strategy, setting up a profile, and simply answering questions and humbly interacting with those discussing your brand. By being a part of the conversation, you can ultimately guide it.
Think about when you're at a party, and there's gossip about someone. If that person were there to address the sortid details, they could easily provide the truth or clarification and the issue would quietly die. If they're not at the party, the gossip circles and distorts and gets embellished and if this were you're brand, you'd be hiding under the porch by now...