Exactly What It Says on the Tin: a blog whose primary purpose is to cover current events.
One type of Current Events Blog will link to a big media news story and then have a comments section on that story. People often read those for the comments. Slashdot, Fark and the Mexican Blog del Narco are examples of this type.
Other blogs are more ideological, and the blog owner will add political commentary to the bottom of an excerpted section from the news story. Daily Kos and Red State are two such examples of this second type. The second type can tend towards Astroturf, since they are often strongly associated with specific political parties.
Still others are just attempts to get Google Ad Sense money, where "current events" is defined as "whatever's on Google Trends that hour."