Basically it's a card issued by the Revenue to a sole trader/company that engages in sub-contract work authorising the principle contractor to pay them the full amount due without deduction of 35% RCT.
You must meet the criteria set out by the Revenue before they will issue a C2. For example you must be fully tax compliant and have all returns submitted and paid up to date.
Have a look at RCT section on the revenue website:
[broken link removed]
Hope this helps