The concept of a responsive design is simple, i.e. you add different elements to a website that can auto-adjust themselves depending on the device it is being accessed. You might have observed that sometimes when you open a site on your tablet or Smartphone, you cannot access all the links smoothly. You need to scroll the screen across horizontally or vertically which makes the design distorted and uneven making it a turn off for the users.
However a responsive website will auto adjust the design and navigation making it easier to view on other devices such as tablet and Smartphone.
Another reason why responsive design is essential is that a fixed website tends to slow down the loading speed on Smartphone if it is graphics heavy.