TL;DR It puts people out of work so there's less demand and we move back down the demand/supply curve towards lower prices/slower increase in prices.
The simplistic version is one idea of the cause of inflation is there's too much demand for all goods as a whole in the economy because there's too much money floating around causing demand to push higher on the demand/supply curve because it's more expensive to produce more of something past a certain point. Making it harder to get loans decreases the money flowing in for some expenditures so there's less expansion in areas like hiring (which when we're near full employment like now usually means having to raise wages pushing costs up and injecting money into the more general market). Thus by increasing the cost of expansion you slow it down and cool the labor market and maybe even cause it to contract.
In the end it boils down to getting more people out of work so they can't buy as much and are willing to accept lower wages meaning it costs less to produce so you might meet the increased demand curve in the middle. It's an incredibly shaky way to try to run the economy but the government has limited knobs to turn and ideally it's easier to target relief at people put out of work because of this than it is to aid the entire population generally.
That's one theory I've heard explained at least. It's incredibly callous to me though because it depends on just putting people out of work and our safety nets in the US are extremely weak meaning you wind up with the fact that a 1 percentage point increase in the unemployment number is associated with a 1-1.6& increase in suicide rates. [0]
[0] https://www.healthaffairs.org/do/10.1377/hpb20220302.274862/....