Curing compost just means to give it time to become extremely stable. This is the point when the compost no longer produces any heat and only gives off an earthy smell. Using compost that has not been cured could damage plants.
To cure compost, simply spread it out over a breathable cloth barrier to protect it from anything in the ground that tries to sprout up into it. Then take a water-proof tarp and cover the pile. The curing compost needs to be kept moist, but nowhere near as moist as an active compost pile. The pile should just be barely moist. To test your compost, place some in a bucket and test to see if it still heats up. If it doesn’t, the compost is cured and ready for use.