Incoming and outgoing links can be double Dutch to some people, but they are vital to your website.
Now a link is a bit of text/image on a website and when you click on it it takes you to another web page or site. A link from your site to another site is an OUTGOING link and a link from another site to your site is an INCOMING link.
Links are seen by search engines as recommendations. So say I am writing a page/article about blue squares and I put in a OUTGOING link to a company who makes blue squares I am effectively recommending this company and their website. It is worth noting here I would get little kudos for providing the OUTGOING link - all the kudos really goes to the website you go to when you follow the link (i.e. the site with the INCOMING link).
The aim of the game is to get as many top quality INCOMING links from other websites to your own site. You can do this by having links on websites of clients, associates, local chambers, networking groups, social networks, business directories, online PR, and so on and so on.
Let the games commence :)