Hi Blast,
To a climber an epic is when things go wrong and keep going wrong so that you are not going to finish the climb under normal circumstances, may need to bail or in worst cases get rescued.

Some examples would be getting off route and having to spend the night in a hanging belay, dropping a rope or your rack and not being able to go up or down, an injury that makes it impossible to continue, a major weather change and you are dressed for summer and suddenly it is winter. As you can see an epic is when things go so bad you wish you were anywhere but there but as soon as you are safe again you are bragging about it at the nearest bar. The possiblitiy of an epic is part of the allure of alpinism but you must work like hell to avoid one or life will get hard real fast.

Lucky for me I have only experienced minor epics such as running out of water, a broken hand, off route etc.
Some climbing epics have taken lives like the guys that got frozen solid in the middle of El Captian a few years ago. It stormed so hard their lines were encased in ice and they were stuck for days. Some died most self rescued and some were airlifted off the rock.
Those were true epics.