For the same reason that dropping the last digit off a normal (decimal) number is the same as dividing it by 10 (ignoring, of course, any non-integer remainder).
In computers, integers are internally represented in binary (base 2). So each digit represents a power of 2 instead of a power of 10 that we're used to with the decimal system.
>> 1
just means to shift all the bits right by one, which is another way of saying "drop the last digit". Since the digits are in binary, that's equivalent to dividing by the base, which is 2.
Similarly, if you need to divide by any power of 2, you can do so using the right shift operator: To divide by 4, shift by 2; to divide by 8, shift by 3; and so on.
Note that internally, it's often more efficient to do a shift operation instead of a division operation, but any compiler worth its salt will do this optimization for you (so that you don't have to write obfuscated code to get the performance benefit -- generally, you would only use the shift operator when your intention is to manipulate bits directly, and use the division operator when your intention is to do math).