A severance deal is a trade: they pay you something, you give up your right to sue them over the layoff.
The money: usually some weeks of pay, often tied to how long you worked there. A lump sum and spread-out checks can be taxed differently.
What you sign away: mainly your right to sue. Sometimes you also agree not to bad-mouth them (ask if that goes both ways) or not to join a competitor (a non-compete, which many states barely enforce).
The clock: you usually do not have to sign today. If you're 40 or older, federal law typically gives you 21 days to decide and 7 days to change your mind after signing.
What to do: read it, see what's negotiable (more weeks, COBRA help, a reference in writing), and for anything big get a quick flat-fee attorney review before you sign.
That's the gist. The full guide below walks through each section and what's negotiable.