Let’s say that one day Kim Jong Un informs the United States he’s about to invade South Korea, and will use tactical nukes. The USA says, “Nope, South Korea is under the US nuclear umbrella,” and Kim laughs and says “Lol, we know you’re not going to retaliate because we have ICBMs that can hit Los Angeles and Chicago and you know your interceptors aren’t reliable,” and hangs up the phone. An hour later, a dozen places in South Korea turn into mushroom clouds.
Or, Russia masses for an invasion of NATO. NATO warns, “We are a nuke-armed alliance, you don’t want to do this,” and the Russian leader laugh, “Nah, we have second-strike ability, and if you use nukes you know what we’ll do to you.” Soon, Russian tanks are rolling into Warsaw. (Now, of course, in real life, Russian nuclear threats are casual and worthless, but assume in this scenario that Russia actually genuinely doesn’t fear NATO nukes one bit and is also itself perfectly willing to use nukes and everyone knows it.)
Or it could work the other way too. Say the USA announces publicly that it will do a Desert Storm type of operation to kick Russian forces out of Ukraine, and Ukraine + NATO + USA also announce they will jointly seize tens of thousands of square kilometers of Russian soil in a land grab, or maybe even seize a bigger chunk of Russian land (but stopping well short of Moscow.) When Russia, predictably, says, “Hey, we have the world’s largest nuclear arsenal!”, America and NATO laugh, “Lol no, we have ballistic-missile subs, you know you can’t take out our second-strike ability and we can make you a wasteland just with our SSBNs alone,” and then the American/NATO/Ukraine tanks begin not only retaking all of Ukraine but also pushing deep into Russian soil.
The whole basis of nuclear deterrence is MAD (mutually assured destruction.) It’s all based off of the assumption that rational actors fear being nuked in retaliation. But what would happen if a nuke-armed nation not only had robustly survivable second-strike ability, but also genuinely did not give a fuck about the risk of being retaliated against? In other words, the aggressor doesn’t fear nukes, but every other nation in the world retains their fear.