The fire flame means that there is a fire happening at the moment. The number inside indicates the level of the fire. The higher the number, the higher the amount of water you need to extinguish it. For example, if you have a fire with level 3, you will need three drops of water. You get that water from the Water Tank in the middle of your city at the Fire Station, which refills automatically. You can expand its capacity or its refill speed. Tap on the red shield button to see upgrades available. If you tap multiple times on the water tank, you will speed up the filling times. 
 
 
The water drop means that your firefighters are already extinguishing the fire or loading the truck with water. The number inside means how much water (drops) have they loaded or used so far.
The big water drop in the fire station shows the capacity of your Water Tank.