This is a question that even embedded systems experts often ask and discuss. There is as with many things a spectrum, and simple definitions are difficult.
My preferred definition is: a system containing one or more computing or processing element that is not a general purpose computer.
Some systems are inarguably embedded within that definition, and include such things as washing machine controllers, telephone switches, satellite navigation equipment, marine chart-plotters, automotive ECUs, laser printers etc.
Some are less easily categorised. A first generation digital mobile phone, is probably certainly an embedded system while more modern feature and smart phones however are somehow different. They can run apps chosen and installed by end-users allowing them to perform tasks not determined by the manufacturer. With increasing capabilities they are essentially hand-held computers and the range of apps sufficient to be able to regard them as "general purpose".
With these more ambiguous systems, it is useful to ask perhaps not what is an embedded system, but rather what is embedded systems development? For example, the manufacturer of your smart-phone deployed on it an operating system, the signal processing and communications stack required for it to operate as a telephone, all the device drivers and stacks for WiFi, USB, data storage etc., and this is certainly embedded systems development. However the guys writing apps for PlayStore or AppStore etc. are writing to a defined common platform abstracted by all that embedded code - that is not embedded systems development by any definition that I would accept, unless perhaps the application were for some bespoke vertical market application - like the delivery signature apps UPS drivers have on PDAs for example - in that environment the "general-purpose" device has been re-purposed as a "special-purpose" device.
With respect to a PC; a PC can be the embedded computing element in a system that is not a general purpose computer. Industrial PCs are commonly found embedded in manufacturing and packaging machinery, CNC machine tools, medical equipment etc. Although they share hardware architecture with desktop PCs they do not necessarily look like desktop PCs and come in many different form factors of both boards, and enclosures. Even within a desktop PC however, there are many examples of embedded computing elements, and embedded software such as the BIOS responsible for bootstrapping the system, the keyboard controller and disc drive controllers for example.