This is a key legal term referring to the contractual ties between parties. Primes often wind up stuck in the middle of disputes. Subcontractors are party to the agreement with the prime, not the government agency. Therefore they usually do not have the right to take action against the government when something goes wrong. However, a prime may sponsor a subcontractor's claim or make its own claim on behalf of the subcontractor.
Primes can find themselves in a sticky spot financially.
If something goes wrong and the agency decides to hold back money, the prime may still be legally obligated to pay the subcontractor. Thus, the prime gets stuck paying for goods and services for which it has not been reimbursed. A prime contractor may be late with a design, for example, while still expecting the subcontractor's finished product by the same deadline. Often both the prime contractor and agency will be allowed to inspect the subcontractor's facilities. And primes may take measures against poor work, such as penalizing tardiness or holding back payment pending government approval of the product.