An irrevocable trust is a trust that holds assets of someone that wishes to pass them along to another or others upon their death or during their lifetime. The major difference between this and a revocable trust is that you can start distributing assets of the irrevocable trust while you are still living whereas in an revocable trust, everything in the trust is distributed to the beneficiary(ies) post mortum. Also, an irrevocable trust involves the participation of the beneficiary(ies) if the one creating the trust wishes to make any sort of amendments to it. A revocable trust doesn't require that a beneficiary become involved if the creator wishes to amend.
People have them if they have a large estate (real estate, stocks, bonds) as trusts provide certain tax breaks that a will does not.