The word "blog" is a hybrid word for the term "web log." Think of it like an online, public journal. The author writes journal entries and other people can read it. A blog differs from a website in that it revolves around continuous posting vs. static information. To continue the metaphor, if a blog is like a journal then a website is like a pamphlet.
Some people/businesses use a blog instead of a website. Much depends on what the site needs to be used for and how much the person wants to spend. In order to have a website, you must pay for a domain name (it's like your personal street address). A blog can be free if you use a blog host (so it's like an apartment, you use it but it's technically not yours). As with living situations, the potential of the blog will be somewhat limited if you use a free host vs. owning your own domain name. In the "house" you can remodel all you like but in the "apartment" you can only really add furniture.