Hi. I'm fairly new to electronics and arduino and I was looking at this tutorial where they connect a resistor on the ground line. The tutorial doesn't explain why they do that and doesn't specify how they came to the decision to use a 10Kohm resistor. It might just be a simple detail but I'm curious and wondering if someone here would be kind enough to explain it to me 
A resistor connected to ground line on input pin is called pull-down resistor, and is used to let the input stable and not floating. Similar configuration can b used with a resistor to positive, called pull-up resistor. With Arduino this is a preferred configuration, since you can use the built-in one (see pinMode() reference. Here the wikipedia page that explain the concept better than me.
Ciao, Ale.
This tells you.
http://www.thebox.myzen.co.uk/Tutorial/Inputs.html
The value is a compromise between using current and being immune from interface.