What does $\ll$ mean?

LL is the suffix for long-long, which is 64-bit on most (all?) C/C++ implementations. So 0LL is a 64-bit literal with the value of 0.

This is similar to L being the suffix for a long literal, which on most 32- and 64-bit C/C++ implementations is the same size as a non-long int. (On 16-bit implementations, the size of int is usually 16 bits, and so the L suffix would indicate a 32-bit integer literal in contrast to the default of 16 bits.)

It is specified in Paragraph 2.14.2 of the C++11 Standard:

2.14.2 Integer literals

[...]

long-long-suffix: one of

ll LL

Paragraph 2.14.2/2, and in particular Table 6, goes on specifying the meaning of the suffix for decimal, octal, and hexadecimal constants, and the types they are given.

Since 0 is an octal literal, the type of 0LL is long long int:

#include <type_traits>

int main()
{
    // Won't fire
    static_assert(std::is_same<decltype(0LL), long long int>::value, "Ouch!");
}