You fond some sites that are very popular, like Matt Cutt's blog and after browsing it for sometime, some thought come into your mind that how this site used to look in early days when it was new. But you can't find anyway to do it, other than asking a scientist for an "Time Machine".
The snapshot are not actually pictures, it's an HTML document generally used by a website, thus if an image was there on an website and later it was deleted from the server then the images won't be showed in the archive of the website. In easy words, they capture the site's HTML, and save it on their server.
You can easily check any website's past by going to Archive.org and entering the URL in this box.Enter your desired URL and click on Take me Back. Now you can select website at what time you want to see.
How to archive your blog also
If you have a new blog or website, even it's 1 or 2 year old, it will be not crawled by archive.org, if you or not anyone has searched the site on archive.org, so if you want your blog or website to be crawled by them, you or anyone has to search your blog in archive.org, after a few months your website will also start appearing on archive.org archives.