See diagrams in attached file.
Let's call the bulb on the left Bulb #1 and the one on the right Bulb #2.
If the switch is closed Bulb #2 will turn off, because the current will be re-routed around Bulb #2 through the switch. This is because the electron charges will choose the path of least resistance, which is the switch, as opposed to the light bulb filament.
Bulb #1 will become brighter. Why? Originally the voltage source supplied a voltage V and a current I through a resistance R, which is made up of the resistances of the two light bulbs added ...
The solution carefully explains and solves the problems.