Imagine, if you will, benchmarking some unknown CPU, and determining that the fused multiply-add operation takes, idk, 17 times as long to execute as an increment operation. We might postulate that there other CPUs out there where it takes a different amount of time — arbitrary amounts of time! Alternatively, we might gain knowledge of the underlying CPU architecture and understand that fused multiply-add is implemented with a certain set of transistors, and that it's fundamentally more complex, though there's room for some variability based on the specific implementation. In such a world this "free parameter" is set as it is for a very specific reason: a transistor arrangement.

We have limited visibility into what's actually happening "underneath" our laws of physics. Some of the values we see could be truly arbitrary. Some of them might actually be controlled by some other field and change over time (though we haven't seen evidence of that so it seems less likely). Some of them could be a deeper artifact of the way the universe works.

If you look at things like string theory, which do try to describe in more detail and dial down the free parameters to just one ("length of the fundamental string" more or less) we are left with something that's frustratingly nonspecific until you locate a more-specific solution within the broader string-theory solution space and call it "the laws of physics." That specific location might indeed seem quite arbitrary; the question might then become, what relation does this hundreds-of-dimensional solution space have with our concepts of physical reality? And can other areas of that landscape be probed in any way meaningful to our experience of physics?