A fecal egg count (FEC) is a test performed by a vet (or laboratory) where they will count the number of worm eggs in a sample of manure. This gives a good idea of the horse's worm load for certain types of worms, but won't tell you if the horse has tapeworms.
If you haven't dewormed with something that kills tapeworms in the last year (or you don't know the horse's worming history) it's a good idea to use one that does. Zimectrin Gold and Quest Plus are two that kill tapeworms.
You might consider discussing with your vet an effective worming program for your area and your horse. Some horses are naturally more resistant to worms (called "low shedders" because few worm eggs are "shed" in their manure) and might only need worming once or twice a year (always at least once a year with something that kills tapeworms), other horses may need to be wormed more frequently ("high shedders")
My horse is a low shedder, and he gets dewormed with the entire barn in the spring using Ivermectin, and then again after the first hard frost in the winter with Quest Plus. I do a FEC between each of these two wormings to ensure he doesn't need any additional worming.