This means that k is greater than or equal to 0 and k is less than 1. If k is a real number, then there are many possible values for k, but if k is an integer, it has to be 0.
Another more compact way to say it is "k is between 0 and 1, possibly equal to 0"
If you're having trouble with the symbol, then an easy way to remember is that with the symbols "<" and ">", the symbol always points to the smaller number.