WordPress comes out with upgrades quite frequently. Many times users are ignoring these updates as they feel they don't really need since the blog is working fine. There are some good reasons that you need to upgrade your WordPress installation.
The biggest issue is security. There are people who target WordPress since it's a very popular blogging platform. These people write scripts to find your site and attack the current version you are using. They will completely erase your site and tell you that you are hacked. If you keep up with the upgrades it will help prevent this.
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At times WordPress has new features. With these new features your plugin developers will start moving on to the new version of WordPress. What this means is that you won't be able to get new features for your plugins or WordPress itself unless you continue to upgrade.
When you do an upgrade, it's generally under Tools > Upgrade and is just a matter of following the steps. If you have an extremely old version of WordPress prior to version 2.0, you may have to export the blog and import it into a newer version of the software since so much has been changed since then.
It's important that you manually backup your database and WordPress files first. You can get to know about 504 gateway timeout nginx, and DNS_PROBE_FINISHED_NXDOMAIN Error.
At times there are corruptions in the update that ruin your database. Without a backup you can't reinstall the blog. Your theme files at times can be lost and that's why it's important to have a copy of everything before the upgrade.