What happens when a PC is switched on and booted up from cold?

When power is first applied like this, the computer starts by passing power to the motherboard and, consequently, the BiOS (Basic Input/Output System - the thing that controls how devices communicate with each other). As power is passed to all of the other system hardware, the BiOS does a check on each of these parts to make sure it's physically able to send and receive communication to and from the other parts properly, among a few other basic sanity tests.

Once the BiOS has confirmed that everything is operating correctly, and there won't be any conflicts or faulty signals, it proceeds to check its boot method. In the BiOS settings, your computer is usually configured to first check if there's a bootable disk in the CD/DVD drive, such as a Windows installation disk, and try to boot the operating system on that. If there is not one, then the BiOS will usually next fall back to booting from the hard drive. The hard drive, among a lot of other components such as your CPU and RAM, fire up, and start loading data needed for your computer to boot the operating system (for most people, that's Windows.)

Once the operating system loads properly, that OS' kernel (the part that actually allows programs to communicate with the hardware, and consequently, the user, through the BiOS) loads hardware drivers - pieces of software that not only tell the computer that hardware is present and functional, but actually how to use it - what to do when the user presses a key on their keyboard, what to do when the mouse sends an electrical signal detailing movement to the left, etc. Once all of the hardware is accounted for and assigned drivers, and the kernel is fully loaded, the software atop the kernel loads. The interface that you can point-and-click in, the code that runs in the background whenever you plug in your media player, etc. Then you may log in and operate your computer.

Amazingly, for most people, this entire process takes less than two minutes - and there are many, many more steps involved that have not been detailed here. If you (carefully) alter the right settings, both in the BiOS and the OS, as well as hardware tweaks, you can shave this down even further. Some people are able to get a computer to a fully operational state in less than 10 seconds.