A blog as stated by urljethosting, is a site where you can share news, information, images and videos etc. For example you may want to share information on a blog about a certain musician and thereafter be posting updates about their whereabouts, their upcoming shows, new music releases and album price, on almost a daily basis etc. A blog post doesn't have to be long: it can be a paragraph long.. You may consider Twitter as a mini-blog. Well known blog sites are: Blogger.com, Squidoo.com, Wordpress.com, Hubpages.com, Triond.com etc.
On the other hand a forum is different from a blog and I don't think there is anything like a "blog forum." A forum is like our site here-ie marketingforums.net
One of the major differences between the two is that: While in a Blog you get BACKLINKS, from a Forum you put a SIGNATURE..