A Droplet, in short, is a VPS, or Virtual Private Server.
A VPS is similar to a Dedicated Server -- you're given
root access and you're able to configure the server to your liking.
Unlike Shared Hosting, however, you're responsible for your VPS and that means you're responsible for updating and upgrading software, maintaining security, installing your stack, installing WordPress and other sysadmin duties.
With Shared Hosting, you receive an account and the web hosting provider handles the rest of the general day-to-day tasks (such as those I mentioned above) in the background so you don't have to worry about it.
Additionally, unlike Shared Hosting, unless you install one of your own, a VPS does not provide you with a Control Panel (like cPanel or Plesk). Without a Control Panel, most of your time will be spent using the CLI (Command Line Interface) using Terminal (MacOS), PuTTy (Windows), or a similar type of shell (if you're running a Linux distro for your desktop).