Please review Appendix B: Operators and Symbols of The Rust Programming Language.
In this case, the double colon (::) is the path separator. Paths are comprised of crates, modules, and items.
The full path for your example item, updated for 1.0 is:
std::usize::BITS
Here, std is the crate, usize is a module, and BITS is the specific item — in this case a constant.
If you scroll up in your file, you'll see use core::usize. use adds the path to the set of items to look in. That's how you can get away with just saying usize::BITS. The core crate is an implementation detail of the façade that is the std crate, so you can just substitute std for core in normal code.
:: can also be used as a way to specify generic types when they cannot otherwise be inferred; this is called the turbofish.
See also: