A blogzine is a mix of a blog and a zine (a small, often homemade magazine). It is a magazine-like thing on the internet that still feels like a blog: regular posts, a personal voice, but dressed up more like a magazine — sections, a look, sometimes several writers. It is a blend word, and not a very common one. You will hear blog, webzine, or online magazine much more. People who make independent web magazines are the ones who say it.