This is probably old news at this point, but more and more the preferred method for consuming content is mobile. Whether this means smartphone, tablet, or some other internet-enabled device, the odds are pretty good that your site will be viewed from something other than a traditional computer. (Although let's be honest, that doesn't really describe anything like it used to either.) Interesting factoid, sure, but what does this mean for your site and for those creating your site?
What the experience was before
There was a time when doing any browsing of the internet from a mobile device was a chore no matter what site you visited. The early internet-of-things was limited to cool kids with a PDA or a curiously-internet-enabled flip phone. This meant that the experience was going to be awful. Resolution on these devices ran somewhere just above what a smart watch today has and color was not always a feature. As the first "smart" phones came out, we saw the mobile web experience improve significantly. It was still a major pain to use, if you put up with it for long, and it was clear that very few websites were going to work at all.
Website developers caught on eventually and they started introducing more mobile-friendly designs for those accessing their site on the go. This was a great start and definitely has built into where we are today, but there was something flawed about this approach. When you visited a site on a phone, you were often whisked away to a completely different version of the site. It was typically a stripped down version of the site and it rarely felt like a deliberate choice.
The tools weren't as easily available to developers either at this time. Our in-house favorite, Drupal, even struggled with presenting sites in a way that worked well on smaller screens. That all did get better in the last few years with more themes specifically built with mobile in mind, but it was a slow build across all fronts.
How the experience should be going forward
Why do users visit your site on the go? Shouldn't your website be just as consumable and useful in that smaller package? We think so too. Responsive design isn't something new, so I won't go into all the details, but the general idea of the modern internet is that your site should be a pleasant experience from smart phone to tv. Users want to get to your site on their phones and not be confused to be presented with an entirely disjointed experience from what they saw at home on their desktop.
More sites are using touch-friendly elements from top to bottom, because you never know how your site will be consumed and it should be awesome no matter which way that happens. Designs are more and more looking at the site from the mobile view to the larger views to ensure that it will work great. Some sites are even starting to transform into app-like experiences that are both familiar and intuitive.
Drupal can help