To get a good idea what unsigned means, one has to understand signed and unsigned integers. For a full explanation of twos-compliment, search Wikipedia, but in a nutshell, a computer stores negative numbers by subtracting negative numbers from 2^32 (for a 32-bit integer). In this way, -1 is stored as 2^32-1. This does mean that you only have 2^31 positive numbers, but that is by the by. This is known as signed integers (as it can have positive or negative sign)
Unsigned tells the compiler that you don't want twos compliment and are dealing only in positive numbers. When -1 is typecast (as it is in the code) to an unsigned int it becomes
2^32-1 = 0b111111111...
Thus that is an easy way of getting a whole lot of 1s in binary.
Use unsigned rarely. If you need to do bit operations, or for some reason need only positive integers bigger than 2^31. Otherwise, if you leave it out, c++ assumes signed integers.