The more tag 'hides' everything below it so that the user has to click the article to read the rest of it. This is good for spoilers and teasers. And it gives you control so that if you write a mixture of short and long articles, you can use the more tag to specify exactly what appears on the front page. The more tag appends a [read the rest of this article] link so the user can click.
The other way to do it, which is the "scorched earth" method, is to replace the_content() with the_excerpt(). This affects every post on the front page and like I said, ultimately gives you less control over things. Haochi got it right. Use the more tag. You can read about it here if my explanation was unclear:
http://codex.wordpress.org/Customizing_the_Read_More
One more thing: get your jargon right. You don't read the "rest of the blogs," but rather the rest of the articles, or posts, or entries. Your blog is the collection of all of those articles/posts/entries. :)