I am a real fan of responsive web design, however there are many more sites (and books) that can explain the topic far better than I can (I’ll list a few at the end of the post).
In short, if you don’t know what it means, it is the idea of a site design that changes its layout depending on the device screen size that is viewing it.
With smartphones and tablets being so popular in the last few years, many more people are browsing the web on these devices, and providing an optimum design for these devices makes sites more engaging, easier to read and better suited to the device.