ERISA preempts normal state court remedies, with its own enforcement scheme.
So, for example, if an insurance company denies a claim for medical treatment, the insured would normally have the right to sue for the benefits, and also for the damages flowing from the claim denial (for example, where the patient dies because she couldn't afford the treatment). There might also be a right to punitive damages.
Under state law, the insured would have to right to sue the insurance company, and during the lawsuit could take full discovery into why his claim was denied. He would have the right to a full trial, where he could call witnesses on his own behalf, call insurance company witnesses to explain themselves, and have the issues decided by a jury of his peers.
ERISA preempts these state law remedies, with its own statutory scheme. ERISA remedies are substantially different than what is seen under most state laws, for example:
There is no right to a jury trial, rather the case is decided by a judge.
There are generally no witnesses, instead the judge relies on the paper record developed while the insurer was deciding the claim.
There is no right to punitive or consequential damages, so if the patient died because an HMO refused to pay for a $1.95 medical procedure, as damages the mourning family would be entitled to - - $1.95.
All this being said, I am tired of the incessant whining about how "unfair" ERISA is. ERISA takes away some things, but there are advantages as well. If your case is any good, you can win in front of a judge, and judges are more reliable than juries. And discovery can be a burden, as some insurers use it to wear down an opponent and discourage litigation by extensive prying into private matters. Under ERISA this would be a rarity. While there aren't any consequential damages under ERISA, it does allow for attorney fees, which most state laws do not. So if you win the other side will pay your lawyer, leaving you a full recovery. And the streamlined nature of an ERISA trial means that you can get a trial date a lot sooner than would normally be the case.
At the end of the day, if you know what you are doing ERISA provides an effective, expedient remedy for a denied claim.