The "collateral source rule" prevents the defendant from arguing that the benefits which an unrelated party paid to an injured person should be deducted from the verdict awarded to the injured person. For example, if the plaintiff in a dog bite case had $10,000 in medical expenses, and $8000 was paid by the plaintiff's health insurance, the collateral source rule would prevent the defendant from arguing that the plaintiff's verdict for medical expenses should be only $2000.
If the collateral source rule strikes you as unfair, think about what the plaintiff paid for the health insurance. To get the $8000 paid by the health insurance company, the plaintiff might have paid health insurance premiums of, let's say, $1000 per month for five years, or 10, or 20, or more. In other words, the plaintiff may have paid out $60,000 for health insurance during five years, or $120,000 during 10 years, etc. to receive the benefit of $8000. And now the defendant wants credit for it. The defendant, who did nothing but injure the plaintiff, wants $8000 in credit against the verdict. Does it still strike you as unfair?
Nevertheless, a number of states have enacted statutes which modified the collateral source rule, or have seen court cases which did the same. Examples include California and Ohio. For an excellent analysis of the law and 50 states, see 50 State Collateral Source Rule Overview by the Harmonie Group / Next Generation.