When you alias a method you give that method another alias. I.e. another name.
@on = true
alias :isOn_New? :isOn?
foo = SomeClass.new
You can use both foo.isOn? and foo.isOn_New?
It is the same method you are calling.
The interesting part about the aliases is that if you overwrite a method any aliases will keep referring to the old method rather than the new one.
Moonpearl mentions the most common usage of aliases, but it can be useful without overwrites. Just look at the standard File class which has both exist? and exists? where writing that method twice would just be redundant. You can also try looking through the Array class and see how many methods could just be aliases of other methods.