To queue for a random dungeon with the LFG tool, you will have to meet the minimum item level requirements for all Cataclysm dungeons in that particular mode. If you queue for a specific dungeon, you simply need to meet the average item level requirement for that dungeon.

The 'average item level' (ilvl) is a computed number that represents the quality of all of your gear.

According to [Wowpedia][1]: 

### Normal Dungeons
 - Blackrock Caverns: 226
 - Throne of the Tides: 226
 - The Stonecore: 272
 - The Vortex Pinnacle: 272
 - Grim Batol: 305
 - Halls of Origination: 305
 - Lost City of the Tol'vir: 305

### Heroic Dungeons
All pre-zandalari heroics require a minimum item level of 329.

### Heroice Rise of Zandalari Dungeons
Thse heroics require a minimum item level of 346.

  [1]: http://www.wowpedia.org/Dungeon_Finder