Prime contractors are companies who work directly for the purchaser of their production, as opposed to subcontractors who typically work for prime contractors.
Multi prime means the buyer has multiple contractors working directly for them on the same project.
Take carmakers for example. The "project" is a car. Company A makes pistons for the engines. B makes airbags. C makes seats. D makes headlight assemblies. etc etc etc. All working directly for the carmaker.
The phrase is more commonly used in construction though. NC, for years, was a multi-prime state for all public building construction projects. A new school, for example, would have 4 prime contracts. General construction, HVAC, plumbing, and electrical.
While this may seem to promote chaos, the legal language of the contracts designated the GC as the project coordinator. As a result, the day to day progress of the job was typically no different than that of a job where everything was under a single prime contract held by the General Contractor.
It was assumed that there were a couple major benefits to the owner via multi primes. Depending on the type of building, the combination of plumbing, HVAC, and electrical can be upward of 50% of the total job cost. General contractors have, for the most part, near zero knowledge of these trades, so there is no point in having them included under the general contract where the GC will add something on the order of 10% to this total. IOW, the public saves money.
And second, each of the primes has to have a performance and payment bond as a condition of the contract. The ability to bond is totally dependent on the financial condition of the contractor. At least 75% of the plumbing, hvac, and electrical contractors out there can't get bonded due to the inability to prove the necessary financials to indicate their ability to carry the job. So, the public gets contractors who have proven stability and financial capability. These contractors are at that point because they're much better than average at what they do, and are also good at running a business. The resulting work is of a higher quality, and more importantly, they are infinitely less likely to go bankrupt in the middle of a job and end up delaying the progress of the entire job for months.
About 20 years ago, public work in NC moved to single prime due to lobbying of our scumbag general assembly by the general contractors. This opened up the hvac, plumbing, and electrical work to bids by every jackleg and his retarded brother, with the net result being the public now gets lower quality work and pays more for it.
Multi prime contracts on public buildings were a much better deal for the people of the state. Industrial construction, which is private, typically avoids the problem of unqualified contractors by having a list of approved major subcontractors. A contract is normally single prime, but the general contractor is required to use companies from the approved list as a condition of the contract.