Coffeescript caters mainly to those who cut their teeth as programmers with Python or Ruby.
I, for one, learned with python, and even though I've used other c-like languages such as c#, php or javascript itself, I always found their syntax cumbersome, verbose and ugly.
It's annoying having to deal with all those curly braces, semicolons and line noise.
Coffeescript borrows the best ideas of these languages while keeping javascript's "good parts" untouched. It simply adds a better, more expressive syntax on top.
There are things that take several lines of code in javascript that can be expressed with one liners in coffeescript, and those are way more intuitive, clear and expressive.
Examples:
How do create an array of numbers from 3 to 10?
myarray = [3..10]
How do you create another array whose items are the previous ones multiplied by three?
newarray = [i*3 for i in myarray]
Just try doing it in plain javascript, and you'll know why Coffeescript is god send for many of us...