Tablets, phones, laptops. The new 3 promises to be mobile friendly from the start.
There is now just one percentage-based grid for Bootstrap 3. Customize for fixed widths.
Improved support for mixins make the new Bootstrap 3 easier to customize.
In simple terms, a responsive web design figures out what resolution of device it's being served on. Flexible grids then size correctly to fit the screen.
The new Bootstrap 3 promises to be a smaller build. The separate Bootstrap base and responsive.css files have now been merged into one. There is no more fixed grid, only fluid.
A big design trend for 2013 is "flat" design. Gone are the days of excessive gradients and shadows. Designers are producing cleaner flat designs, and Bootstrap 3 takes advantage of this minimalist trend.