If something is incessant, it keeps going and does not stop. English speakers nearly always use it when they are tired of the thing: incessant rain, incessant noise, incessant questions. The word carries a small complaint. You would not usually call a lovely song incessant, even if it played for a long time — that would sound as if you wanted it to end. It is a rather formal adjective. In everyday talk people more often say non-stop, or it just wouldn’t stop. Continuous is a cooler, more neutral cousin: a weather report can say continuous rain without sounding annoyed. Incessant rain sounds as if you have had enough.