Let's say I have a 11W bulb in my home, connected to a 220V power supply. What exactly does it mean that this bulb is 11W? As far as I know, the Wattage is determined by the formula $W = V * I$, so it really depends on the voltage and the current. The current is determined by the resistance: $V = R * I$. So I don't understand what is the meaning of a 11W bulb?
$11 W$ means the bulb uses 11 watts of power when it's operating at the rated voltage. If you run it for an hour for example, it will cost $0.011 kWh$, and your power company will bill you for ___ (check your local electricity prices).
You can also calculate how much current the bulb will draw since you know the voltage, as well as the resistance of the bulb (from $P = V^2/R$).
$11\rm\,W$ means that at its working voltage, on average over a period electrical energy is converted into other forms of energy, heat and light, at a rate of $11\rm\,J/s$.
One has to be careful when quoting the resistance of a light bulb as a bulb's resistance depends on the applied voltage with a higher applied voltage increasing the temperature of the filament which in turn results in the resistance of the filament increasing.