How do domestic appliances work at different voltages when the applied voltage is same for every appliance? Generally, the electric connections at home are in parallel combination. How is it possible for a geyser(220 Volts) and a cellphone charger (5 volts) to operate at different voltages in a parallel combination?

 A: The charger accepts one voltage as its input, and produces another voltage as its output. This could be done with a transformer or any number of other conversion techniques - for example, in a switched mode regulator the voltage is connected very briefly to charge a capacitor, then disconnected again. It keeps repeating this to keep the output at the right voltage. By smoothing out the voltage and current bumps with inductors and capacitors you get a nice 5V supply from a 110 (115, 120, 220, 240) V supply - even when the supply is fluctuating.
You can think of it as trying to fill a leaky bucket from a fire hose. You have to turn the hose on briefly to fill the bucket - and as it starts to empty, you turn the hose on briefly again. If the hole in the bucket is bigger (you are drawing more current from the supply) you have to turn the hose on more often. You will make less mess if you can turn the hose on more gently - this is where inductors play a role (they prevent a sudden surge of current); and the size of the bucket represents the capacitor: if you have a large capacitor, you only need to turn the hose on occasionally, and water will flow out at a nice constant rate.
Incidentally, in the US the power supply to a house comes in two flavors: 120 V and 240 V. In fact they supply 2 lots of 120 V of opposite polarity. If you connect an appliance across the two, it will experience 240 V; if you connect between just one "live" and neutral, you get 120 V. High power appliances (water heater, dryer, oven) need the larger voltage.
