The reason your lights dim when you use your hair dryer is because the circuit has too many things using the amps capacity of the circuit.
A hair dryer can use between 1,600 watts to 1,800 watts of electricity so it's normal for the hair dryer to dim lights if the lights are on the same circuit as the hair dryer and something else.
In the bathroom a house is supposed to have a dedicated bathroom circuit for hair dryers and curling irons and other high wattage electrical appliances used in the bathroom.
But some older homes and even mobile homes have the bathroom circuit on the same circuit as the lights and some bedroom circuits.
Some homes may also have 15 amp circuits and 14 gauge wire while new homes have 12 gauge wire and 20 amp circuits.
If your circuit breaker is not tripping and the wires are not getting hot then it's okay for the lights to dim some when the hair dryer is on.
However if the lights dim too much then it could be a problem.