The block function is your first line of defense to get rid of things you don't want to see on Tumblr, whether it's simply a blog posting unpleasant things in a tag you follow or somebody actively stalking or harassing you. If you block one of your followers, the block feature works as normal, but the person you blocked is far more likely to notice it.
On Your Dashboard
Once you block a blog, you will never see posts from that blog on your dashboard again. This includes tag pages, search results, note pop-ups and any kind of notification, such as the one you get when somebody reblogs from you. If somebody else reblogs a post from somebody you've blocked, however, you will still see that post -- both on your dashboard, if the person is somebody you followed, and in tag pages and search results.
On Her Dashboard
The only way for somebody you've blocked to see your posts is to go directly to your blog's main page, since once you've blocked her, your posts will no longer show up anywhere on her dashboard, including on tag pages and search results. If somebody reblogs one of your posts, however, she'll see it just fine. This means it's quite easy for her to figure out that you've blocked her, since all she has to do is notice that your posts show up on your blog's main page but not on her dashboard and put two and two together.
Somebody you've blocked can still send you messages, but whether she's following you or not, you will never receive them, whether they're asks, fan mail or post submissions. She will not receive an error message stating you've blocked her, however. There is only one exception to this. If you send an ask or a fan mail message to somebody you've blocked, you will receive any response she sends as if you hadn't blocked her, even though the block remains in place.
On Following and Followers Lists
When you block one of your followers (which Twitter also refers to as "ignoring"), you will no longer see her name on your followers list, although she will still count toward your followers total. On her end, you will still appear on her list of blogs she is following; she will also see the real value for how long ago you posted, which gives her another way to figure out that you've blocked her.