<p>What does a JIT compiler specifically do as opposed to a non-JIT compiler? Can someone give a succinct and easy to understand description?</p>

A JIT compiler runs
after
the program has started and compiles the code (usually bytecode or some kind of VM instructions) on the fly (or just-in-time, as it's called) into a form that's usually faster, typically the host CPU's native instruction set. A JIT has access to dynamic runtime information whereas a standard compiler doesn't and can make better optimizations like inlining functions that are used frequently.
This is in contrast to a traditional compiler that compiles
all
the code to machine language
before
the program is first run.
To paraphrase, conventional compilers build the whole program as an EXE file BEFORE the first time you run it. For newer style programs, an assembly is generated with pseudocode (p-code). Only AFTER you execute the program on the OS (e.g., by double-clicking on its icon) will the (JIT) compiler kick in and generate machine code (m-code) that the Intel-based processor or whatever will understand.