A Knowledge Base is ment to organize your random notes into a structured form - wiki-alike, but not the same more ridgit structure.

I see the use in a KM mainly when you have to document things for which you don't want to run separate apps or are building yourself a strong basis of documentation. You could document your insurance numbers much the same way that you do your home server configurations. Now, in a KM, you organize them to a degree and maybe your insurance eventually goes digital and offers you a FIDO setup. Now you might reference your infrastructure from within your insurance. You can do that in a wiki too, but a KM usually makes inter-connection a little easier.