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Can anyone tell me whether having “links” on your website are really important to getting business traffic?
I have a shopping website and what to know how I can get traffic to sell my products. How do move up in ranking on search engines to get noticed?

when search engines crawl your site for content, they look at the links as a part of your content. suppose someone searches for xyz.com which is not your site, but you have it linked on your site, now you are in the results for their original search. Also search engines like to see that you are not just a dead stop, but have relevant content linking to other content.
References :

Take it from me, a guy with a PR7 website with around 600 daily visitors, you need inbound links from high PageRank sites because that is what the engines use to decide where to place a site in its listing. However, these are super hard to get, so what I do is buy expired domains that already have good pagerank and use them to link to my existing site. This way, not only do I get the free traffic that comes with the domain, but I also get to piggyback on its pagerank. A great site that I have found for finding high PR expiring domains is:

http://www.webaddresslive.com
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You should try Adweb 8.0 It automatically submits this to websites, directories, link sites etc., helps you make
changes. Within a week I noticed a big difference…I would say my traffice doubled. I wish I had found it
sooner, I wouldn't have had to waste all of that time doing it manually. Oh well, you live and learn. Good Luck!

P.S. I have tried other programs and had no luck. This is by far the best one I have tried. It was well worth it.
References :
http://www.mycashjunction.com/?2532:3892