If you want to add an external library to Unreal Engine, then you will probably want to make it a plug-in. In that case, you can see how other plug-ins link by browsing their source code.
Definitions
Defines passed to compiler, e.g. WITH_EDITOR, FOO=1, etc.
PublicSystemIncludePaths
Haven’t used, include paths for platform headers probably?
PublicLibraryPaths
Paths in which to search for static libraries
PublicAdditionalLibraries
Names of static libraries to link against, e.g. foo.lib for Windows.
PublicDelayLoadDLLs
Names of dlls which should not be loaded instantly on program startup, but will wait until their symbols are first needed. This lets you load them yourself during your module startup routine, where you can specify their location. Means you don’t have to have them deployed in the same directory as the program binary. I think Windows platforms only, not sure.
RuntimeDependencies
Paths to any extra files you want to distribute with packaged builds. They wind up at same relative path in package as they are in the project folder. Most common use is third party dlls.