The Blogs module leverages the standard security used for all documents. You can find more details in chapter Permissions for modules and documents.
You can manage the posts if you are either owner of the blog, blog moderator, global administrator or if you are granted with the Manage comments for the Blogs module in the Administration -> Permissions dialog. The Display module permission enables the Blogs module in the user interface.
The blogs in the My Desk -> My blogs dialog are displayed only to the blog document owner.