Each virtual or dedicated hosting machine has its own Os and works independently from the hosting servers of other clients. Updating the OS is usually neglected, but doing that may have lots of advantages for your websites. The most significant reason to employ the newest version is that patches are typically released to deal with security holes inside the Operating System code, so if you don't install the updates, you risk individuals with destructive intentions to exploit these holes and to get access to your content. OS updates are also released for improved performance of the system as a whole and for far better compatibility with the hardware available on the market, which could directly impact the efficiency of your websites. If the performance and the security of your scripts is the reason to update them, you may also know that their most recent versions require an updated Operating System so as to function properly, so keeping the Operating system up-to-date is always a wise idea.
