In this case, the double slashes are absolute "paths" relative to the top of the workspace, and the part after the colon is a relative "path" to another Bazel target.

I put "paths" in quotes because these are meaningfully different from the true filesystem equivalents; avoiding confusion with real absolute and relative filesystem paths is probably why they made their own syntactic mini-language.

[The sibling reply to mine, referencing Piper and Perforce, goes into a bit more detail on the specifics and the origin of the // prefix.]

What would the better way have been for them to do this?

The ":" is a bit different, e.g. just "//lib" means "//lib:lib" - e.g. points to the "lib" target in /lib/BUILD file, while "//lib:hello-time" points to "hello-time" target in /lib/BUILD file. So not having the ":name" in "//dir:name" means name="dir" - e.g. "//dir:dir" - at first this is strange, but then you get used to it. Your default target is named after the folder it's sitting in.