A growth factor is a general term for any substance that stimulates cell growth, cell division or cellular differentiation. They are most often some type of protein or steroid hormone, and have a bewildering tangle of names which may or may not include the phrase 'growth factor'. Growth factors are secreted by a range of different sources, from damaged cells to the kidney and various glands to tumors. They bind to specific receptors on the surface of those cells that are designed to accept them, and stimulate increased activity of various and sundry sorts.
Many growth factors have other functions in other contexts, so you may find reference to glucose phosphate isomerase (for example) as both a growth factor (outside the cell) and a part of the glycolysis metabolic pathway (inside the cell). The term 'cytokine' is occasionally used interchangeably with 'growth factor', but while many cytokines are growth factors, not all are.