Deep pocket is an American slang term; it usually means "extensive financial wealth or resources".[1] It is typically used in reference to big companies or organizations (ex: the American tobacco companies have "deep pockets"), although it can be used in reference to wealthy individuals (e.g., Bill Gates, Warren Buffett).
In the context of a lawsuit, the deep pocket is often the target defendant, even when the true (moral) culpability is with another party because the deep pocket has money to pay a verdict. For example, a lawyer may comment that he or she sued the manufacturer of a product rather than the seller because the manufacturer has the deep pockets, meaning it has more money than the seller with which to compensate the victim and profit the attorney.