The official definition for this term is two or more tasks running simultaneously. What this means in practice is that with a processor such as the 80386 or better and some clever software, you can run more than one program at a time. You could be typing a letter in a word processor, while also checking the stock market figures from CompuServe and recalculating your company's profit margin in a spreadsheet.
In an advanced computer system that might be used to run a company, there are several processor chips inside each of which can run one program. This is a very fast and efficient way of processing when the demands are high, but for home or small office use, you don't need more than one processor. To achieve the same result on your PC software switches very rapidly between each program. For example, if you are running, say Word, CompuServe CIM and Excel, then the software would divide the processor's time into tiny slices and give each a slice. This way, although the processor is servicing three programs, it's fast enough to look as if they are all running concurrently. Microsoft Windows and Novell DOS 7 both do this and let you runseveral programs at the same time.
