Why does cheap food help prevent inflation?

I’ve always been under the impression that abnormally low agricultural prices can mitigate inflation, but I really have no idea why this is; is anyone else familiar with this axiom?

Falling agricultural prices will (other things being equal) reduce food prices. Food is a biggish part of the basket of commodities that make up the CPI. It is also possible that reduced food prices will mitigate wage demands which will reduce cost pressures in other sectors.

Right. Inflation indexes are roughly speaking just an average of what is going on in different parts of the economy. Falling food prices can offset things like rising energy prices. Food prices that remain flat still result in lower inflation than if they had gone up like other things.