Why does brightness of the bulb decrease when a heater is connected in parallel to it? Whenever we connect electric bulb in parallel with a electric heater, the brightness of the bulb decreases, but later it acquires its original brightness in spite of parallel combination (in which voltage across bulb remains same).Why?
 A: When the heater is cold, its resistance is low, and a large current will flow through it. This causes a voltage drop in the room because the copper wiring  connection to the mains grid also has some resistance.
After a while, the heater gets hot. This causes an increase in the resistivity of the heater wire. It will draw less current, the voltage drop will become smaller, the light bulbs will get a bit brighter again.
How large the voltage drop is depends on the "internal resistance" or the "output impedance" of the connection to the mains grid.
A: 
Why does brightness of the bulb decrease when a heater is connected in
  parallel to it?

Given the lack of context, the most probably answer is that the added current through the heater causes the voltage across the parallel combination to drop due to the resistance of the wiring feeding the circuit.
As a practical example, for a recent home project, my wife and I installed an electric 'fireplace' that contains a 1.4 kW heating element which is roughly 11.7 A from a 120 V (AC) source.  Assuming the wiring from the breaker panel to the outlet had just 1 ohm of total resistance, the voltage at the outlet should drop by over 10 V when the heater is on.
Using a Kill A Watt Meter, I measured the voltage at the outlet as 122V when the heater was off and 116V when the heater was on.  Since, in this room, the receptacles and lighting share a common circuit breaker, I could detect a slight dimming of the room lights when the heater was turned on.
