I am feeling really down and I thought of going for a walk to think my life through.. maybe skip a rock at a lake or something..and right then I remembered about some comics in which Superman was going to walk around for some reason. What was the whole walking thing about? Why he did it and did it accomplish anything?

I'm assuming you're referring to Grounded? Don't dwell on it too much. There were a few meaningful issues at the start but then it died down with little purpose.

Instead of responding to the world's big problems, Clark decided to focus on the smaller ones.

Yeah, Grounded was pretty bad overall. Basically, Superman walked through a lot of major American cities and, mostly, engaged in debates with ordinary people. I think the writer, JMS, was trying to get across a message about personal responsibility and not waiting for others to fix your problems for you. Which is not a message I necessarily disagree with, but he went about it pretty heavy handedly. He basically set up a bunch of straw man arguments which put his points in Superman's mouth while giving embarrassingly weak arguments to whoever was arguing against him so you never felt like JMS was being fair. He also oversimplified real world issues like illegal immigration and wrote some moments that were out and out bewildering. Finally, after realizing the reviews were bad, JMS dropped Superman and the storyline he started giving a weak excuse about how busy he was with his Earth One graphic novels. Writer Chris Roberson took over and did his best to save it. He wrote JMS' material off as Superman being depressed, brought in some interesting cameos (Batman, Wonder Woman, Elliot S! Maggin), and tried to inject some imagination into it, but the damage had been done. Grounded ended up going on for too long, losing focus, and ending with a whimper. If it accomplished anything it sped up the new 52 revamp by convincing DC that they had a massive Superman-shaped problem on their hands.

It was an experiment on how to write the most boring Superman story imaginable.