Blogger's posts are by default displayed in the reverse chronological order (i.e. the most recent post is displayed first). This means that, as and when you write new posts, the visitors to your blog's homepage get to see those new posts.
A sticky post is a post that gets stuck to the homepage and remains at the top no matter how many other posts you write. This is very useful if you want to make your blog index page similar to that of a normal website, which has the same homepage all the time.
The trick is to manipulate the post date and time of the particular post that you want to remain as the homepage. All you have to do is to set the date and time of that post to somewhere in the future. For example, if this post is forward-dated to, say, July 26th 2010, it will remain on the index page for another year. The farther you set the post date, the more it stays stuck at the top.
The "Post date and time" settings are found at the bottom of the post editor window, and are illustrated in the figure below.
Remember to first publish your post in the normal way and then to modify the post date and time from the edit post mode. If you forward-date the post before its initial publishing, then it will go as a scheduled post.
Other than creating the pseudo homepage, this trick is useful to create notices that you want to stay on top for some time. For example, if you are organizing some event that occurs in two months time and you want all the readers to your blog during the next two months to see that notice, you can forward-date it by two months so that it will remain at the top until the event is over.
Another thing you might want to do is removing the displaying of the post date and time from the Post Page Options section. Otherwise, your visitors might get the feeling that they have time traveled to reach your blog.