What are Static Sites?
Static sites are web sites that don't use a server to generate content. They're just plain HTML, JS, and CSS. Because they don't need to be generated by a server, they can be hosted on Content Deliver Networks, which are more lightweight, secure, and easier to manage than traditional servers.
Why Static Sites?
Because they are hosted on CDNs, and are flat file, static sites are much faster than traditional server-based sites. They're also less prone to errors and are far more secure (no server to SQL inject/hack). Moreover, static sites can still be dynamic: by making AJAX calls (requests to external resources), static sites can still load dynamic content from databases and servers. So they aren't a limitation.
Looking for a more wordy and comprehensive breakdown? Checkout the original article here.