Palpatine's Nostril had a few meanings, the super giant destructive lasery weapon thingy and the, less than pretty body part and a Force attack.
The Super Giant Destructive Lasery Weapon Thingy (Palpatine's Nostril Weapon)
Palpatine's Nostril was a Super Giant... (You get the idea) or simply a Super Weapon, like the Death Star. It was referred to by Han Solo when he wondered what the empire would call their next super weapon. He was right.
The Body Part (Palpatine's Actual Nostril)
Palpatine's Nostril had Palpatine's Nose Hairs. It was old a wrinkley like the man himself.
The Force Power (Called Palpatine's Nostril)
As palpatine had the POWAAAAAAAAAAHH of the force he had his own special force powers such as this, which fired Palpatine's 'snot' at opponents (or people he frequently got anoyed with) at a very very very very very high speed.