In short, it is a bug that makes your private information ---> public.
To protect yourself as much as possible, you should consider changing a few of your passwords. Mashable.com has put together a very comprehensive list of accounts that may or may not be affected by the bug.
Here's a summary of suggested accounts for password changes:
Social Networks
- Facebook, Instagram, Pinterest, and Tumblr
Email Accounts
- Google and Yahoo + Gmail and Ymail
Stores and Commerce
- Amazon, Etsy, and GoDaddy
Videos, Photos, Games & Entertainment
- Flickr, MineCraft, Netflix, SoundCloud, and YouTube
Financial Accounts
- USAA
- Box, Dropbox, GitHub, IFTTT, OKCupid, Wikipedia, Wunderlist
Jewel's Random TidBits - If any of these accounts are linked to an email account you do not check often, you may want to log-in now. Many of these websites/companies sent out informational emails on how the Heartbleed bug may affect your account.