Responsive design is where an object changes in response to a users actions. E.g. An electric window in a car that won’t close if there is something in the way, a child’s fingers. Someone has put some intelligence into the design. This is now happening on the web.
This is happening with the search engines, where searches for ‘Leicester square cinema’ provide you with a list of films, times and durations. A local map with location stick points and cinema phone numbers. This is the search engine's response to your search... They are guessing that in the first place you don’t actually need the cinema websites. Responding to the user in real time.
Can your website do this? At work we use laptops, in front of the TV we use Tablets, and when we are out and about we use Smartphones. The screen sizes are all different and your website needs to respond to this. To ensure your website is responsive we can test on all the platforms and devices your viewers use.
Adaptive web design is different to Responsive design in that a website built as an Adaptive web design will respond to a set number of defined screen resolutions, whereas Responsive design is fluid and so will (should) work for any size and is able to adapt to new devices as they develop.