To work on an Epic Building/Project you first have to have reached level 24. When you do so the epic building(big clock) gives you a brief explanation and points out a building with a winged helmet above it. When you put the money down and start it gives you a measuring stick of sorts. An epic building always works with one specialization, be it Beach, Entertainment, or one of the others. Each of the specialization buildings will give you a amount of an item they need. When you can fill that amount and do so, it gives you 1-4 points, depending on the building. When you reach 10 points you have a bronze epic, 80 points a silver, and 160 a gold.
It's hard to explain but epic points lead to epic buildings which lead to speed up tokens. You may have already used them by level 24. The turtle ones speed up production by 2x, Llama by 4x, and Cheetah by 12x. For more information on epics, there is a pinned post at the top of this forum page. Hope this helps!
