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:
- 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
All pre-zandalari heroics require a minimum item level of 329.
Heroic Rise of Zandalari Dungeons
These heroics require a minimum item level of 346.