An author can mark their own posts or comments as deleted. This will remove the post from the common user interface (like: Steemit, etc..) and remove the post from most API calls but the post will remain as part of the blockchain history.
Delete a Post or Comment
When logged in, a "Delete" link may be shown to the author of any post or comment along side of the the "Edit" link. This link may be missing if this operation is no longer possible (see below). Clicking on the delete link will show a confirmation dialog prior to making the actual delete.
After a Delete
The author's "Delete" will remove the post from all feeds (hot, created, trending, etc..) including the users own feeds (Blog, Posts, etc). The post will basically be removed completely from the standard web view.
A comment or post can be deleted only if it does not have any replies and it does not have a net positive vote (positive payout). If a post has a positive payout it is adding value to the platform and therefore should not be deleted.
You may track this feature at: https://github.com/steemit/steemit.com/issues/20