Tier links are basically a web of connecting strings that drips "link juice" or authority from one page to another.
Money site - your main domain that you focus on.
Tier 1 - these links point to your money site directly.
Tier 2 - these links point to any/all Tier 1 links.
Tier 3 - these links point to any/all Tier 2 links.
Tier 4 - at this point, the Tiers have become so diluted that at Tier 4, the quality begins to dwindle.