What the evidence reasonably supports
Mood and alertness. Cold immersion produces a substantial and sustained rise in circulating noradrenaline, and the subjective effect of that is the alert, level feeling people describe for two to three hours afterwards. This is the most consistently replicated finding and it is the honest reason most people keep doing it.
Perceived soreness. Cold water after hard exercise reliably reduces how sore people report being over the following days. Worth noting that reduced perceived soreness is what the studies measure, and it is a genuine benefit regardless.
What it does not do
It does not burn a meaningful amount of fat. The brown-adipose research is real and the effect size in adults is small enough to be irrelevant next to anything you do with food or movement.
It does not boost your immune system in any sense that word usually implies. There is some evidence of fewer self-reported sick days in cold-shower trials, which is interesting and is not the same claim.
And it does not detoxify anything. Nothing does; you have a liver.
The one thing it works against
If you are lifting weights specifically to build muscle, cold immersion in the four hours after a session appears to blunt the adaptation. The inflammation you are damping down is part of the signal that tells the muscle to grow.
This is a real and repeated finding and it is the single most useful thing on this page for anybody training seriously. Plunge on rest days, or hours later, or before you lift. Not straight after.