how exactly does it increases the current?
Where did you get the idea that is does?
Is it possible to control servo's and motors with just the Arduino?
Servos - yes. Motors - no.
If not the why?
Because they draw too much current.
Whats the maximum current an Arduino can handle?
In or out? Which Arduino? A typical pin can deliver 40mA of current, although long term safe ratings are lower than that.
How about the Shield?
In or out? The shield doesn't boost the current of the Arduino, so the same limits apply.