Links are essential elements of any web page. Like the age rings of a tree trunk, links are revealing a lot about a website to search engines: The popularity of a website (based on the number and popularity of pages linking to them) and things like trust, spam, and authority. If a site is trustworthy it tends to link to other trusted sites. Most search engines reward trusted sites, so building up a good link profile and using internal links the right way is very valuable.
Links in general
Backlinks or 'inbound links' are links that are directed towards your website from other sites. The number of backlinks is an indication of how popular your site is and of how important/trustworthy search engines perceive your website to be.
Google, will give more SEO credit to websites with a large number of 'quality' backlinks. If you want your site to come out on top on Googles results page for a certain search query, you should strive to get a lot of good backlinks from other trustworthy and relevant sites.
Anchor text in backlinks - (High SEO value)
Include a keyword in the anchor text of a link. An anchor text is the visible text in the link bewteen the <a></a>
<a href="http://www.example.com">This is the Anchor Text</a>
Make good use of synonyms, keyword stemming to achieve variation in the anchor texts on your page. Duplicate use of the same anchor text is penalized by Google. Make sure that you use anchor text that is actually relevant to the destination page. The page you are linking to should at least include some of the keywords that you are using in the anchor text.
Mind who links to you - (High SEO value)
A link is not just a link. It matters WHO links to you. Certain sites have greater Google PR and are considered 'reputable'. Links from link farms or the like will harm you, so avoid inbound links from these kinds of sites.
The more links from similar sites like your own, the better. Here too, the reputation of the sites that link to you is important. Equally important is their anchor text (and its diversity), the lack/presence of keyword(s) in it, the link age, etc.
Anchor text of internal links - (Medium SEO value)
Remember to add anchor text when you link bewteen your own pages on your website. These links also counts and adds to a positive SEO effect, though not as much as the anchor text of backlinks.
Older backlinks counts more than new ones - (Medium SEO value)
The age of a external link linking to your page is a positve factor. The older the link is, the better effect for your page. For some search engines adding many new external links to one webpage in a short time suggests buying them.