what do App Memory, Wired Memory, and Compressed mean?
This wonderful Apple Support article says it all: https://support.apple.com/en-us/HT201464#memory

I'll give the short version here:

There are three different types of memory, as you have noticed - wired, app, and compressed. Each of these types do something slightly different.

Wired memory
Wired memory refers to memory that cannot be taken out from RAM. The contents of wired memory cannot be paged to your disk (swap), and are used by programs. This memory can't be used anywhere else, and stays in memory until whatever is using it is terminated. Usually, this memory is used by OS X's core functions and belongs to the kernel. In a way, you might consider it meta-memory, the memory that oversees other memory.

this other question on wired memory and its answer expands more on wired memory and its use.

App memory
App memory refers to memory utilised by open/background processes and applications.

Compressed memory
Compressed memory refers to memory (that isn't being used), which OS X automatically compresses to free up RAM for other processes to use.



This may be unrelated to your question, but I thought I'd expand on it:

Swap memory
Swap memory is RAM contents that have been paged out to disk to free up RAM within memory modules. The entire concept of swap memory is sort of "expanding" RAM by taking parts of your hard disk and writing RAM contents into it.

Additional resource: Apple Developer Library: Virtual Memory