In comtemporary parlance (where the abbreviation PC is often used), the term generally refers to either a desk-top (fixed location) machine, or a lap-top (portable personal computer).
A note-pad is effectively a small lap-top, but one without a keyboard, using a touch-screen for user input. Recently, portable PC's have merged with portable phones, producing the now-ubiquitous smart-phone.
Changing technology made personal computers both possible, and also desirable, instead of sharing a mainframe using time-sharing - the previous model of computer usage.
One principal driver of personal computers was the advent of high-performance displays (in particular, bit-mapped displays). While allowing all manner of powerful new applications, they used a lot of computing power to drive them.
This melded well with a fortuitous contemporary development, that of the microprocessor. Some early 'personal computers' (in the general sense of the term, that they were intended for use by one person at a time) were built out of many integrated circuits, held on a number of PCBs, like other computers of the era.
Very slightly later, the first PC's (in the sense of 'small computer which an ordinary person could afford'), using the first microprocessor appeared. Eventually the two merged; the Apple Lisa, although not commercially successful, pointed the way, and the Apple Macintosh confirmed the unification of the two groups of 'personal computers'.