user mode versus kernel mode
Think of a power tool with a safety guard. In normal use the guard is locked on and you simply cannot reach the spinning blade - that is the safe setting most of us stay in. There is also a service mode where a trained technician removes the guard to do dangerous work. A CPU has the same two settings, and it enforces them in hardware: a restricted setting for ordinary programs, and an all-powerful setting reserved for the kernel.
Concretely, the CPU is at every instant in one of (at least) two modes. In user mode - where all your programs run - the hardware forbids certain instructions and certain memory accesses: a program in user mode literally cannot run the instruction that halts the CPU, cannot touch another program's memory, and cannot talk to a disk controller directly. In kernel mode (also called supervisor mode) those restrictions are lifted; the kernel runs here and can do anything. The CPU itself checks the current mode on every instruction, so a misbehaving user program is stopped by the hardware, not merely by good manners.
Why it matters: this hardware-enforced wall is what makes a multi-user, multi-program computer safe and stable. A buggy or malicious program in user mode cannot crash the machine or read your bank app's memory, because the CPU will refuse and trap into the kernel instead. The only way a user-mode program reaches the privileged side is through a controlled doorway - a system call - which switches the CPU into kernel mode at a fixed, trusted entry point. Without this two-mode design, any program could do anything, and one bug could take down everything.
Try, in user mode, to execute a privileged instruction like the one that disables interrupts, and the CPU refuses: it raises a fault and hands control to the kernel, which typically kills your program. The same instruction inside the kernel just runs.
Same instruction, different mode, opposite outcome - the CPU enforces the wall.
'Kernel mode' is a CPU privilege state, not a place in memory. Being in kernel mode means the CPU will run privileged instructions now; it is separate from (though related to) the idea of kernel-space memory.