"Cummis counsel" is legal jargon, or a "nickname," for a private attorney who is retained by an insured person at the expense of his insurance company, in a case in which the person is exposed to a court judgment in excess of the limit of his insurance policy.
The best way to explain this is to give an example. Let's say that you have a $1 million insurance policy against personal liability. One day, you learn that you are the defendant in a lawsuit for $2.5 million. This is $1.5 million less than your insurance, which is limited to $1 million. Because of this gap, you technically are at risk for the difference between those two amounts. You stand to lose money from your own pocket.
For that reason, the law says that you are entitled to the services of an attorney who is accountable only to you, not to the insurance company -- and the insurance company has to pay for both attorneys, theirs and yours. The "nickname" for your private attorney is "Cummis counsel," so-called because it was the Cummis case that established your rights to a private lawyer under these circumstances.