Generally speaking, it's a service to your "customer", i.e., the visitor of the site.
Nowadays, many people surf the world wide web through WiFi hotspots. For example, when they're having a coffee, eating a burger somewhere, et cetera. Even some public transportation services offer free WiFi.
Most public WiFi's don't have any encryption at all and everyone with a WiFi enabled device (laptop or the likes) can "sniff" all the traffic of such free WiFi access point. Even the WiFi access points with a shared password isn't secure! (Because it's a shared password! )
Obviously, I have no idea what for kind of information your site contains, but generally speaking: nobody needs to know what I'm doing on the world wide web. Even if it's useless information, I would like to keep this between myself and the server operator (the latter is unavoidable unfortunately ).
And now with Let's Encrypt, you can offer this service for free! As in, free beer!
The implementation of a Let's Encrypt certificate depends a lot on how your server is organised. I.e., is it a site run on a shared hosting environment? Or does it run on a (virtual) server of its own? If so, what OS? Et cetera et cetera.