What is the iLevel on Path of Exile?

I've seen several times mentioned "iLevel", which is not shown on the statistics of items. What is it and how to know the iLevel of an item?

iLevel, or ilvl, is the item level - basically an internal variable that affects what sort of affixes and other properties the item can be generated with. Extremely low ilvl items will have a very limited number of potential affixes they can use, while high-ilvl gear can be generated with powerful modifiers and sockets.

Details on ilvl, including how to check: http://pathofexile.gamepedia.com/Item_level

List of item affixes: http://pathofexile.gamepedia.com/Affix

In recent versions of Path of Exile, holding down alt when hovering over an item will show you its item level.

As Majuju answered, the item level is used to determine which effects are possible on your item.