Importance of resistor
That resistor, where positioned, is called a pull-down resistor, and if replaced by a straight wire, that circuit would short out when the switch was closed.

The purpose of this is that when a digital input pin is not connected, it floats, and if the switch were open that pin could see upwards of 2v floating value from external and internal noise. With Digital circuitry, any value in this float range can be invalid and return invalid results. 

A pull down resistor will generally have a very high ohmic value >5kohm, as to allow as little current pass as possible. Here, you are shorting the pin to ground through the resistor so it will not have a LOW value when the switch is open, instead of possibly invalid.

When the switch is closed, you will have 5v passing through switch into the pin, to be read as a HIGH value, also sending 5v across a 10k or so resistor to ground, consuming only .5mA of current.

It you want to see what I mean by a floating value, debug the output of any analog pin with a wire going nowhere, and watch as the value changes. Try touching the wire, now add a pull down to ground, or try pulling it up to 5v and observe the behavior.

Happy Arduinoing!