Gone are the days when people viewed your website from the comfort of their den on a big monitor.  Chances are that visitors are using a tablet or a smartphone.  Your site needs to look good on a small or large screen.  If your site isnt mobile ready, Google will actually reduce your ranking!  Your website needs to be seen properly no matter what it is viewed on.  
To some, this means taking the lowest common denominator approach, using the smartphone view for all devices.  Pull out your smartphone and take a look at the typical non-responsive site.  What you will see is the entire width of page squeezed into the small screen, the text is unreadable and the images are unrecognizable.  Expand the page to where you can read the text.  You will probably  need to scroll left and right just to read one line.  Not very friendly is it?
What is really needed is for your website to recognize what it is being viewed on and adjust accordingly.  This usually means scaling the font to a readable size and reflowing the text.  
You could solve the problem by having several versions of your website.  The site then would only need to recognize the type of device that it is being viewed on (desktop, tablet or smartphone) and display the appropriate version.  The problem is that you now need to maintain at least three versions.  Not very efficient!
Of course, there are many other considerations.  Whole books have been written on the subject, so here are just a few:
  • Leave out the awkward content, if it doesnt fit on a smartphone, it may not belong on the website
  • Images need to be scaled to fit but do they work at the different sizes?
  • When columns dont fit side by side, they need to flow vertically, but does the content get mixed up?
  • Menus need to be adjusted (what do you do when you have one on the left and another across the top?) so that the visitor can click it easily
  • Does the site have anything that doesnt work on a smartphone.  Flash was big for a while but it is not supported by Apple devices
  • Bandwidth on mobile devices is limited compared to desktops, if its slow to load on a desktop, it may be intolerable on a smartphone
The answer is to design the website to respond to the device that is being used to view it.  A good solution needs to combine technical techniques with good design practices.