Links are important for two things. Firstly, they draw more people to your site. Secondly, they can improve your site ranking, which means your position in Google is improved, which means you get yet more visitors.
It's not just a case of a high number of links though. Rank is based on the quality of those links too. Links from sites set up just to spam links, or sites which don't have good rank themselves (due to low-quality content), don't mean much; links from a respected site with plenty of good content do.
Another factor to consider is relevancy. A site about model trains linking to another site about model trains, or model trucks, or real trains, is seen as relevant, and so the link is better quality and improves ranking more. A site about cakes linking to one about petrol is likely to have a low relevance, and so does not help ranking much.
Because of this, it is generally better to have a small amount of good quality, relevant links than it is to have hundreds of low-quality, irrelevant ones.
One of the best ways to work out which sites you should be trying to get links from is studying other sites similar to yours, or that you are already linking to, and trying to find the sites that link to them. You can then look at these sites yourself and work out if they'd be a good link for you, and then contact them about it. Remember to be polite. They are doing you a favour.
A linking strategy to avoid is reciprocal linking. Google does not count links that bounce back and forth as much as it does one-way links. In some cases, such as when pursuing a very high-quality link, it may be worth considering, but most of the time it is not.
Finally, remember that a linking strategy should be backed up by high-quality content. Good content not only encourages people to link to your site, but means that when people get there, they're more likely to stay.
