Grossly simplified: Fed contractors must pay their workers the "prevailing wage" to have their bid accepted. Without a rule like this, a contractor can easily under-bid the competition -- especially union competition -- by reducing costs by paying their workers less than the prevailing wage.
The rule change being rolled back was made by Regan back in the 80s. They used to determine prevailing wages by saying any wage at least 30% of workers in a region are making is prevailing (which at the time amounted to something like a 70th percentile wage), but Reagan changed it to be a majority. If there was no clear wage that was paid to this large a number of workers, you would instead determine an average wage, which after the rule change tended to be used most of the time. This meant one shady contractor underpaying their workers directly reduced the wages of these federal contract workers, since averages are now being used.
Before the rule change, you would typically find a wage that at least a third of workers were earning in a region and that would be the minimum prevailing wage. It only took a few good employers (edit: or one decent trade union) to push that prevailing wage up. After the change, large and powerful employers could easily suppress the wage for their whole region by pushing down the average.
Many states have their own prevailing wages for state-funded contracts, and if you live somewhere that actually gives a shit about its citizens, it's very high.
It makes for great investment in things like infrastructure when the government provides grants and low-interest loans, essentially free money, to local municipalities. They get the infrastructure, as well as all the local, well-paying jobs that the work brings. And that money stays local because it's usually local contractors and engineering firms doing the work.
As I understand it, the prevailing wages are established regionally, meaning areas with very strong unions (for example) will tend to see MUCH higher labor cost for their government contracts. Which is a big part of the change Reagan made. By making union markets so much more expensive than "abused worker" markets, it meant big contracts that weren't married to some locality would tend to be pulled from those union markets by the bidding process, punishing those places for daring to care about their workers.
Fortunately, a lot of infrastructure IS necessarily local.
There is a dark side to that kind of "free money for infrastructure", though, which we're seeing in tons of American cities these days.
The eternal growth mindset has led to many cities building more than their tax base will ever be able to maintain. More roads, more sewers, more firehouses, more electrical lines. Especially true with the nearly-unlimited faucet that is state DOT money, allowing endless major road and highway expansion even if the project makes zero economic sense. It makes it seem like a no-brainer for towns to build eternally outwards and get shiny new subdevelopments instead of investing in the communities that are their economic engines, since the federal money tends to vastly prefer new construction.
They are established locally, but the federal government calculates their own (as required by the Davis-Bacon Act). Some states may or may not have similar laws of their own, and calculate their state prevailing wage differently than the federal government (in labor-friendly states, it'll be much higher in general).
At least with respect to the contracts I'm familiar with, the higher of the two (between federal and state wage rates) must be paid. In the case of my state, they're higher than federal rates 100% of the time. And they're very fair, it's great to see folks that work that hard get paid like that.
So basically it's like federal/state minimum wage, but for government contracts.