Updating is Highly advised , since newer version Fixes bugs, brings New Features , provides Stability. Upgrading Kernel provides better support for your hardware and performance too.
And Security updates are important to keep your Ubuntu secure.
One way : Use Update Manager to update your system .It will classify list updates under categories as Important Security Updates , Recommended Updates and Other Updates
( eg. PPA's)
Second way : through terminal
sudo apt-get update && sudo apt-get upgrade
This would be the best way to update your Ubuntu
Also if you want to upgrade your kernel , do it after the above process through
sudo apt-get dist-upgrade
Or combining all above ,as All-in-one command.
sudo apt-get update && sudo apt-get upgrade && sudo apt-get dist-upgrade
You can see the Ubuntu security notices here listing fixed vulnerabilities through updates , resolved mostly through security and other updates.
example : Fixing bugs through updates.