Infeasible things are impossible, or too complicated to actually be done. Your idea of staging a city-wide game of Capture the Flag is probably infeasible.
After several frustrating attempts at walking your cat around the neighborhood on a leash, you might finally decide the idea is infeasible — it's just not going to work the way you imagined. When something is feasible, it's entirely possible. Feasible comes from the Old French faisable, "that may be done," from the Latin root facere, "to make or do." When you add the "not" prefix in-, you get infeasible.