Colligative properties
Here's an answer without complexity which I read in my book. When you heat a liquid in open vessel, its molecules turn to vapours, but the atmospheric pressure above is pushing these vapours down. Some vapours would have enough energy to tackle this atmospheric pressure and would get away from the liquid leading to evaporation. Only some particles at the surface would have enough energy but when vapour pressure reaches atmospheric pressure, all liquid molecules have enough energy to counteract the pressure on them and thus liquid can form vapours from the whole bulk of the liquid leading to boiling.