Behavioral Retargeting or Post Visit Targeting, is when you display an advertisement to a website visitor after they visit your website on a network of sites. This is done by placing a pixel on the visitors computer and when that pixel is seen by one of a number of online publishers, it displays your ad in real time.

For the clients that I have worked with and of all the non-search ad mediums, this is by far the most effective form of online targeting.

Pros:
-Target Consumers after they see your product, remind them of you while they are making their buying decision.
-Targeted branding
-No wasted ad space to non-targeted demographic.

Cons:
-Some privacy concerns. It is not illegal, but privacy right activists are trying like hell to do so.
-Limited to the amount of visitors that come to your site. Example: if you have 100 visitors a day coming to your site, the most banners you will be displaying is 100 as you are only displaying banners who have come through your site.