This is a process that can be explained in hundreds of pages, but typically a boot process involves in powering all the devices in a computer in a certain order. When you press the power button (soft start), the CPU is initialized based on clock ticks, then sends signals to the north and south bridges. It verifies if the battery is OK, then it advances to POST boot which involves in checking the RAM for consistency and then looks for other devices attached to the system. If everything is OK, in most of the cases you should hear a short BEEP. After this process, the BIOS looks for an OS to load. The CPU and RAM is then used to load the files, drivers, peripheric devices etc., until the system boots completely to desktop.
