The kernel memory in the task manager is a part of the total memory available in a computer that is blocked off for the operating system's processes. The total memory consists of the RAM (random-access memory) and the virtual memory. The "Paged" under kernel memory in the task manager refers to the part of the virtual memory that is dedicated to the kernel, while the "Nonpaged" refers to the dedicated kernel memory in RAM. The value for "Paged" and "Nonpaged" varies because some kernel processes are moved from the RAM to the virtual memory and vice versa.
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The idea of kernel memory comes from the computer structure, which has a kernel layer that is responsible for the core processes to run the operating system. When you run your computer during startup, the kernel layer identifies the processes needed to load your OS. These processes are essential and thus kernel memory was developed as part of memory management to ensure that there is always an available and dedicated memory for core processes.
Nonpaged Kernel Memory
The nonpaged kernel memory in task manager refers to the kernel memory that uses your RAM. Operating system processes initially use the RAM during startup, but after it has been loaded, memory management transfers some of the processes to the virtual memory to free up your RAM for other applications. Your computer actively manages the memory by continuously swapping OS processes between the RAM and the virtual memory. The processes that use the RAM are called nonpaged, while those that are transferred to the virtual memory are called paged.
Paged Kernel Memory
Virtual memory is used to take off some load from the RAM, making the RAM available for other applications. It uses your hard disk space by creating a filein your root folder named pagefile.sys. Similar to RAM, a portion of the pagefile.sys is blocked off for kernel memory. Idle processes used by the OS are transferred to the virtual memory. The information that you see in the task manager for "Paged" under "Kernel Memory" is the amount used for the kernel.
Available Physical Memory
The "Available" information under "Physical Memory" of the task manager is the free space of RAM that can be used for other applications. This value will never be zero because some processes will always be transferred to the virtual memory.
Virtual memory extends the limited capacity of RAM. For RAM to always have available memory for running applications, some processes are transferred to the pagefile.sys. The total virtual memory currently used by your computer is the "Total" under "Commit Charge" in Windows Task Manager. This total is the sum of the "Mem Usage" you see in the "Processes" tab.