To make a difference in any endeavour or field means, broadly, to have a significant effect.
Until recently the expression was usually encountered as make the difference, typically the difference between a positive outcome and a flat or negative outcome. For instance, we might say that a star sales manager “made the difference” between her company breaking even and turning a very nice profit.
In the last ten or fifteen years or so, however, the expression has been most often used in exhortations to “make a difference” in your community: to give generously not just of your money but of your time and your expertise to make your community a better place for everyone. Companies proclaim that they want to “make a difference” by supporting local charities, or by providing advice to start-up businesses or by training displaced workers in new job skills. And the rising Millenial generation of young people is popularly supposed to have a more earnest desire to “make a difference” than their self- and family-centered parents and grandparents.