An advertorial is an article that is paid for and usually contains information about a product/service (but not always). Lots of blogs offer advertorials and in general the links within these articles should be nofollowed.
Advantages: If you've got a relevant audience to what your advertising partner is looking for then you can often make a pretty penny from advertorials.
Alongside this, you're able to place a full disclaimer at the start of the post to ensure that your readers understand that you've not written the post.
Disadvantages: From my experience, a lot of companies looking to purchase advertorials will prefer you not to disclose that it's an advertorial and also dofollow the links. My advice here would be not to do it, but it's your own decision.
I've done both in the past and I must admit that I made a lot more money from the non-disclosure/dofollow link option, but times are changing and you could find yourself in hot water with the big G.