Before updating your server to version 1.16.1, you'll need to be prepare first. Why prepare? It's because 1.16.1 recently came out and all of the plugins you use for your server may not work for 1.16.1 or may disabled itself if a untested version of Minecraft is detected. Most plugins for 1.15.2 do appear to work in 1.16.1.
We can download Spigot 1.16.1 right now, you can download that at GetBukkit.Once downloaded, go to your downloads folder and rename the file to "server.jar".
Now we can upload this to our server. Make sure you've already stopped the server before continuing. Once the server is stopped, delete the existing "server.jar" file from your server files and upload the new one we just downloaded by GetBukkit. Once the file is uploaded, boot up the server and check for specific errors, also make sure all plugins are working.
You can also see what plugins are disabled for 1.16.1 by typing "/plugins" and see what plugins are labeled in red. Greens ones are good to go.
If everything worked out smoothly, then your server has been updated to 1.16.1.