You can also copy and replace the server files, but there is a gui available as shown below.
Visit one of the following site (I recommend Yive's mirror) and download the server jar file that you want to update your server to. Make sure that you update to the correct server type (spigot -> spigot) and not (spigot -> taco).
Also make sure that you also don't download an api jar!
(make sure that it does not has 'api' in its name)
Now it's time to select the server jar file you downloaded in the previous step. You can either drop it onto the form or you can browse for it with the 'Select file' option.
Click 'Update' to start the process. This won't take long.
All done! Wasn't that easy?