One of the hidden benefits of blogging about your work that may not be immediately obvious (assuming that you write a blog about your own research) is that it gives you a record of your progress and your journey as a genealogist. It's a curious thing about humans, but when we learn things, we often focus so much on what we are doing at the moment, that we don't get any sense of the progress we have made since we started out. In school we learn in groups, and what we learn becomes things that "everybody knows". We learn things, and we internalize them, and the information becomes "stuff we know"; we don't think about how we learned it. Even if we graduate and get a degree, we may have a sense of accomplishment, but it doesn't necessarily give us a sense of our progress because we are moving along with a group all doing the same thing.
Once we are out of the classroom setting, and working on our own, it is only when we meet someone who knew us "back then", and we discover that our teachers or fellow students don't know all those things that we have learned since we left school, that we get a sense of how much we have learned since we left them. But if you write a journal, you have a record of your journey. You can go back and review the work of your younger self and see your own progress.
If you write this kind of blog, you don't even have to post it online to get the benefit of it. A friend of mine, hearing me complain about not being able to find good research journaling software, suggested I set up a blog locally on my Mac and to record what I did that way. I wish I had done so; it would have been a backup record of all the things I had found, which I'm now having to reconstruct after losing a database and moving to a new computer. I could have retraced my steps, and looked over the research of the early days with the experience I have now, picking up missed leads and clues.
However, it's not necessary that a blog be about your own work. One of my favorite bloggers writes about her hometown (she no longer lives there).
She may indeed make contact with relatives, but she can also interact with others who are interested in the same place -- thus her blog serves as a virtual genealogy society and local historical society. It's not only for people doing family history, but attracts a wider audience.
As far as I can tell, there is no overlap between her family and my husband's family, but any posts she makes about town history, the geography, the architecture, etc. are valuable to me, since I've never visited the town. No one person can know everything there is to know, so when readers comment, she too can learn about resources she may have neglected, or simply have someone to talk to about her hometown.
The other benefit of writing a blog, or starting a website, or any posting online like here on SE, is that it helps you focus your thoughts. Writing for an audience, even an imaginary one, makes you examine a problem again in a new way -- used effectively, it's a great way to break down brick walls.
The choice of which venue to use for your writing -- a website, a blog, SE, a mailing list, or some other forum -- depends on the individual person. But the big advantage that a blog (or another kind of dated diary) has over these other forms is that it leaves a chronological record behind so you can see where you've been and when you got there.
P.S. some thoughtful commentary about blogging vs. other means of establishing an online presence here: The Death of the Blog, Again, Again, Again from science fiction writer John Scalzi, on his blog Whatever.