We are asked a lot about this - mainly because stylus pens are becoming quite a popular promotional gift to complement the growing use of smart-phones and tablets.
Well, the best way of putting it is that a capacitive screen (which the vast majority of devices use these days) is electrically sensitive - as your finger touches the screen, the screen's electro-static field builds a small capacitor (a charge) between your skin and the screen, and the screen detects this exactly.
It is very precise, can handle more than one input on the screen (i.e. multiple fingers) but has the disadvantage that it won't detect a touch from a finger wearing a glove (as typical glove material does not conduct and therefore won't allow the electrical charge to build up).
That's where the silicon tip on a stylus pen comes into it's own - it allows the current to flow through un-impeded.
As a technical aside, the conducting material you touch the screen with doesn't particularly have to have low resistance - as long as it conducts! Try using paper on your smart screen (paper conducts but has relatively high resistance to the flow of electrons) - it will still work.
A resistive screen (not used much now) actually has layers in the screen that detect pressure changes. Not as sensitive as capacitive, not as able to detect multiple inputs, but at least you can use gloves. As you can imagine, really best used for devices that run simple applications on the screen that can work in all weathers (e.g. a delivery man!).