Blogger's Android app is really basic and doesn't offer too many features. It's mostly useful if you want to write a new post, since you can't edit the existing posts. The editor only lets you enter text and include one or more photos. You can add some labels and geotag your posts, taking advantage of your phone's GPS. If you haven't finished a post, you can always save it as a draft, but you won't be able to publish it from a computer because it's only saved locally.
Blogger's blog mentions that Blogger is a new sharing option, so you can easily share a photo from the Gallery or a web page. "By switching to the List View, you can view all your drafts and published posts that you wrote using the app." Unfortunately, you can't edit existing posts.
All in all, Blogger's Android app offers very few features and I would only use it to write short posts or to share photos from a trip. Maybe Blogger's team should also develop a mobile web app which could be updated faster.
Android Market link: Blogger's app.