The image above illustrates how BigPipe can help even slow-to-render pages deliver usable content to the browser very quickly. If you have a block in a sidebar that pulls in some data from an external service, or only one tiny user-specific block (like a "Welcome, Jeff!" widget with a profile picture) that takes a half second or longer to render, Drupal can now serve the majority of a page immediately, then send the slower content when it's ready.
To the end user, it's a night-and-day difference; users can start interacting with the page very quickly, and content seamlessly loads into other parts of the page as it is delivered. Read more about BigPipe in Drupal—it's currently labeled as an 'experimental' module in Drupal 8.1, and I'm currently poking and prodding BigPipe with Drupal VM.
Also, in case you're wondering, here's a great overview of the difference between ESI and BigPipe.
There are a few caveats with BigPipe—depending on your infrastructure's configuration, you may need