Something that's cutting-edge is the very latest or the most stylish. If you always covet the newest kind of cellphone, you could say that you like cutting-edge technology.
The adjective cutting-edge often describes new advances in science or technology — a hospital might advertise its use of cutting-edge cancer treatments, for example. Art can be described as cutting-edge as well, if it uses innovative techniques or does something completely new. The word cutting-edge has only been used in this figurative way since the mid-1960s; before that it literally meant "the edge of a tool's blade."