Lithium batteries have a very specific range of operation, and do not tolerate excursions outside that range.
Charging (or discharging) at too high a rate will cause the battery to fail because it increases battery temperature, and because it encourages the growth of dendritic Lithium metal which will short circuit the cathode and anode (increasing temperature). Overcharging and discharging can also cause failures, but most Li-Ion batteries have an internal chip to prevent these situations.
Initially a failing battery will "puff" due to gas generation from the breakdown of electrolyte, but the cells are vented to prevent them from exploding. If the failure is allowed to progress (for instance if the battery is left on charge at too high a rate), the battery will ultimately achieve a condition of "a highly energetic exothermic chemical reaction". Temperatures well above 300ºC are possible - and you can't put it out since it's not combustion, it's a chemical reaction.
It's hot, and it generates a lot of smoke, and it'll set things nearby on fire, but it doesn't actually "explode".