A sponsored post is essentially where a company or individual will pay to sponsor one of your articles. This will often be related to their company or product/services and will include a reference link to them within a disclaimer in the post.
For example, a furniture company might sponsor an article about the latest design trends of the year, and the post might feature some of their products.
Advantages: There's a lot of money to be made from sponsored posts. Within certain niches, companies will be willing to pay a lot of money to have their products/services/brand featured on your site.
This is particularly relevant if you have a really good community on your blog that will engage with your site and drive through a lot of referral traffic to other websites.
Another advantage is how easy it can be to attain some of these opportunities. One method that I've used within my own travel blog in the past is to target internet marketing agencies with a specialism in the travel niche - you'd be surprised how easy it is to find them with a simple search.
If you want a more advanced technique then check out my link prospecting process.
Disadvantages: There are a few down-sides to this type of content. If you're going to be monetizing your individual blog posts as 'sponsored' articles then you might find that your readers will be turned off. It can really cheapen the article, especially if you're not disclosing clearly.
Secondly, a lot of companies will ask you to make the link a 'dofollow' instead of a 'nofollow' link, which breaks Google's Webmaster Guidelines. On top of this, you will often find that the company/individual isn't keen on you disclosing that the article is a sponsored post, which can leave you in a tricky situation.