Safewords are very useful for situations where some words need to mean things other than their traditional meanings, typically in BDSM
Sometimes in BDSM, you want to be able to say "no" or "stop" and have the scene continue.
For example, if you really like being whipped but it makes you whimper like a little girl, you wouldn't want your sadist to put the whip down when you started crying. You really want them to keep going.
Safewords are usually strange words that are very unlikely to be naturally said during the course of the scene, such as "octopus" or "peanut butter." A common scheme for safewords is the traffic light pattern, in which green stands for "everything is just fine," yellow stands for "something is a little weird, don't stop but slow down (or check my bindings, or something)," and red stands for "stop right now, this is very bad."
In a perfect world, no one would ever have to use a safeword. But it's better than not having one just in case you need it. (If you're unsure about this, just ask me for my story about not having one.)