Minimalism is the most modern form if digital design. It includes many philosophies which reject the idea of dense, populated page areas. When you build a minimalist website this requires stripping many of the odds-and-ends which are not required. Similarly minimalist logo ideas are put together through simple brush strokes and smaller patterns.
Check out some of my examples below to get a better idea of minimalism in action. Branding your company is such an important topic, and logo design goes right along with it. Keep your eyes open for new branding opportunities wherever you can think of. And when designing for a minimalist audience, consider some of the techniques applied in the logo examples below.