They are version numbers, and are there for two reasons; so that you can safely and easily upgrade your libraries, and so you can have more than one version of them installed at the same time.

When there's two numbers there's a major and a minor version. libncursesw.so.5.6 has major version 5 and minor version 6; in theory any minor version of the same major version is compatible without recompiling, so programs that linked to libncursesw.so.5 wouldn't miss a beat if you upgraded to 5.7 for a bugfix. If you had an ancient program demanding version 4, you could safely install a 4.x library alongside the 5.x ones, and nothing but that program would use it.

Sometimes programmers don't think that far ahead though; they might link to a too specific version, breaking their program every time you upgrade a library, or link to libncursesw.so itself, causing crashes and/or strange runtime errors when the library's not what they expected.