The Physical Memory is the amount of actual memory installed in your computer that Windows is currently able to access. The total of 8191MB is 8GB, so you have 8GB of RAM installed in your compuer.
Currently, 5417MB (5.29GB) is used by the caching features of Windows 7 (file buffers, mapped files, superfetch, etc.). Cached memory is memory in use that can be dropped and retrieved at any time since the data exists elsewhere (on the network or on the disk, etc.).
Your Available Memory (6202MB or 6.05GB) the size of the cached memory plus whatever memory is backed by the page file. Windows 7 will sometimes "pre-swap" memory out to the page file before it is requested. This memory is "stale" (hasn't been accessed in a while) and is unlikely to be needed right away. By "pre-swapping" it out, it exists in both Physical Memory and the page file. If the program that allocated that memory needs it, there is no swapping involved since it is still in memory. On the other hand, if a different program makes a request for a large amount of memory and Windows has to start swapping memory out, it can just "drop" the pre-swapped memory since it is already in the page file. This helps make Windows seem snappier since it doesn't have to write it to disk before granting the allocation request. It looks like Windows has "pre-swapped" 785MB (Available Memory - Cached Memory) to the page file.
Free memory (819MB) is memory that is not in use by anything on the system. It is 100% completely unused. Usually you want this to be as low as possible because unused memory is wasted. (Of course, it could also be that with that much RAM, Windows just couldn't find something to fit in there - my 2GB system has 464MB available and 13MB free.)
Kernel Memory is a chunk of memory that is assigned to the core of Windows, the kernel. This memory is used by Windows for keeping track of low level objects (like window handles, file handles, GDI handles, etc.) and for drivers (like your video card, network card, etc.).
Paged Kernel Memory (known as the "Paged Pool") for the Kernel is treated mostly like normal memory. It gets allocated when needed by drivers (or Windows directly) and can be swapped out when necessary to make more room.
Nonpaged Kernel Memory (known as the "Nonpaged Pool") is more delicate. Nonpaged memory is specially allocated so that it will never be swapped out in any occasion. This is necessary when the system is processing a device interrupt at such a high level it can't access the disk to swap memory back. In fact, if it did get swapped out (or the driver is accessing the wrong memory) this will lead to the well known BSOD "Page fault in non-paged area".
There is an awesome article written by Mark Russinovich, Pushing the Limits of Windows: Paged and Nonpaged Pool, that explains the paged and nonpaged pool of memory for the Kernel. If you're interested it is definitely worth the read!