It means "left shift" in binary. This corresponds to adding a specified number of zeros at the end of the binary representation of the original number. So 1 << 0 is binary 1, 1 << 1 is binary 10, 1 << 2 is binary 100, 1 << 3 is binary 1000...
If you think about the meaning of place value in binary, this is exactly the same as raising two to a specified power. Each time you shift one place further left in binary, it's equivalent to multiplying the existing number by two. So repeating that a specified number of times is multiplying by a specified power of two.
One funny thing about Mersenne primes is that, as a result of what you describe, they are exactly those primes whose binary representation consists of a prime number of ones!
The smallest Mersenne prime, three, is binary 11, while the next largest is seven (111), then 31 (11111), then 127 (1111111). The next candidate, 2047 (11111111111), is not prime.
If you think about the meaning of place value in binary, this is exactly the same as raising two to a specified power. Each time you shift one place further left in binary, it's equivalent to multiplying the existing number by two. So repeating that a specified number of times is multiplying by a specified power of two.