This is a phrase that was popularized by U.S. President Dwight D. Eisenhower during his farewell address. In it, he warned to beware the dangers of the "military-industrial complex". The initial drafts of this speech actually include the wording of "military-industrial-congressional complex," which is really more what he was talking about, but the congressional portion was removed to not upset politicians. This is an important point to make, as congress is an important player in the complex.

Anyway, the idea is that the way these three things interact creates huge conflicts of interest between them and it generates a feedback loop of corruption and wasteful spending. So you have politicians in congress that want to continue to be voted in - the easiest thing they can do to pad their resume is point to jobs that they've generated for their constituents. Since they're in the government, they can vote for bills that will award big contracts to companies that are based in their districts. Since the US military is so huge, most major contracts are defense related. This generates jobs for the citizens of that district, generates big money for the company that gets awarded the contract, and helps the politician get re-elected. So everyone wins, right? Well, not really. When this starts happening, there's a feedback loop that occurs that starts to inflate the prices of everything because everyone wants a piece of the pie - corporate lobbyists spend a ton of money on politicians, politicians want to spread out the jobs so it becomes difficult to effectively build things, and the military likes fancy expensive things. But the really big issue is that it promotes extremely wasteful spending; when it's in everyone's best interest to just fund a ton of military projects, things that get funded are not actually beneficial to the military capabilities of the country and instead it starts focusing on whatever benefits corporations and politicians the most, because the military stops actually being the main beneficiary of military spending. And once we have all this bloated military spending and equipment, suddenly using it in conflicts to justify its existence becomes in the best interest of politicians and corporations that benefit the most from it.