Quality Level (or "QL" for short) is used in TSW to display the relative level of equipment in the game.
The levels range from 0 to 10, with 0 being the weakest and 10 being the most powerful.
Many items can also be upgraded with Glyphs or Signets. Using Glyphs or Signets on an item makes it more powerful, or more specialized (adding Heal Rating, Penetration Rating, etc).
Additionally, there are QL10 items you can buy from your faction specific Vendor by using either Black Bullion (only gained from running Dungeons in Nightmare Mode) or by using Black Mark of Venice and White Mark of Venice (gained from doing PvP). You can buy upgrade Toolkits for these items (again using Bullion or Marks). Each item can be upgraded 4 times - taking it from QL10 to QL10.1 and up to QL10.4
Note here: You can not use PvP gear with NM-Dungeon Upgradkits and vice versa. You can only upgrade PvP gear with PvP Upgradkits bought with Black Mark of Venice and White Mark of Venice.
Running Nightmare(NM) dungeons, the first Bosses in each Dungeon drops a purple item that is the equivalent to QL10. Some harder bosses drops purple Items of QL10.1 and the final boss drops purple items that are the equivalent to QL10.2
While not a technically correct, many Players use "QL" as a shorthand to describe the level "Level" of their character. In general, this means the average Level of the Gear (Weapon and Talismans) they have equipped. For example, the page on Dungeons says you should be "QL2-3" to run The Polaris (Dungeon).