In short, you'll stop getting fixes for security problems.
When a security flaw is discovered in a piece of software during its security support lifetime, the vendor (Ubuntu) will endeavour to release an update to the software which fixes the security flaw.
After the security support lifetime has elapsed, the vendor will no longer provide updates which fix security flaws, even if new security flaws are discovered.
From your point of view, after the support lifetime elapses, you will not notice anything happening at first, except that software on your system will cease to receive updates, and this may leave your system vulnerable to security flaws even if they have been publicly reported.
Thus, it is important to upgrade to a newer version of Ubuntu which is supported, so that you can continue to receive security updates.
You can upgrade Ubuntu at any time to the next version, or from one LTS version to the next LTS version, whether security support has ended or not, though it's a good idea to do so before that happens so as not to leave your system vulnerable.
If you choose to install the LTS version (the most current one of which is 14.04), this will receive support for 5 years, instead of the usual 9 months. This is a better option if upgrading at least every 9 months is too frequent for you.