Dead cap is salary cap space a team spends on players who are no longer on the roster. It happens because signing bonuses are spread across the length of a contract for cap purposes, so releasing or trading a player accelerates the unpaid remainder onto the books at once.
The mechanism is close to amortisation in football accounting. A signing bonus is paid up front but charged against the cap in equal slices across the contract, so cutting a player early leaves the remaining slices with nowhere to go, and they land immediately.
It is the main reason NFL teams keep players they no longer want. If releasing someone costs more cap space than keeping them, the contract has effectively locked the team in, and the decision is financial rather than sporting.
Teams can spread the damage by designating a release after a certain date in the calendar, which splits the charge across two seasons instead of one. That is a delay rather than a saving, and a club that leans on it repeatedly ends up paying a growing share of its cap to players who have gone.