You've probably already encountered plugins or themes that don't support php5.6 that you've used or even might be using now.
Why is moving to php 7.2 important?
First of all, PHP versions 7.2 or 7.3 are several times faster than 5.6. This actually means that the same page in say WordPress (or any php page) is processed (loaded) 3 times faster than on version 5.6.
This was achieved by the developers of PHP, they realized that php5.6 was very slow and they had to work on it and finally succeeded. So as you can see the php versions jumped right to version 7.0 from 5.6 because the versions in between didn't quite turn out the way they envisioned.
The second thing, and perhaps the most important one, is that php versions 5.6, 7.0 and 7.1 are no longer supported or updated for them. We certainly use CloudLinux, so there are security patches for those php versions, but there are no more improvements for them.
You must have seen that WordPress now recommends PHP version 7.2 during installation, and with that a large number of plugins already work on new versions of PHP.
How to upgrade your site to a newer version of PHP?
By simply logging into cPanel and through the MultiPHP Editor option, you will be able to tick your domain (or more if you have them) and select the desired version from the drop-down menu. You have changed the php version with one click.
After the change, the site stopped working?
If the site stopped working or reports a 500 error after the change, it means that something on your site does not support the newer version and you need to replace or change it urgently. Why urgent, because it is a possible security flaw on your site.
How to find and fix the error is shown in this post: