8 year mil NK analyst turned 2 year civilian NK analyst here, with a 'secure' perspective. I roughly agree with the common ideas about leverage and all, but I want to introduce an angle many don't consider.
Will SK invade tomorrow? No. Do I think the domestic SK public (and global audience) understimates the growing internal impetus of SK and Japan to take a much more militant stance against NK rather than relying on sanctions upon sanctions? Yes.
People have pointed to the events over the last 5 years as "peninsula sheninagans as usual". They are anything but. Ever since 2010, where SK was hit with double whammy of KPAN sinking Cheonan (don't feel like debating conspiracy theories right now, don't bother, we aren't going to agree) and the YP island attack, the government/military has taken an undeclared hardline stance against NK; when President Park today said "provocations will be met with retaliations", she's not bluffing. And NK knows it. Front area combat arms, naval forces, and air force commanders have been delegated alot of authority to respond to threats violently on their own initiative (eg without phoning up to the MOD or Blue House for permission). The clearest public example was the landmine provocation a little while ago. NK plants reasonably deniable landmine, SK says it will resume propaganda operations over the DMZ, NK threatens it will shoot a loudspeaker and subsequently tests the waters by shooting two shells at one, SK responds with a full battery's worth of response and promises all further retaliation will be equally disproportionate... and as an end result, NK backs down and offers one of the few public apologies it has ever offered to any nation, let alone its "puppet enemy". There is a changed dynamic on the peninsula, and even if the people don't realize it the course of their daily lives (I wish I could tell you the specifics of how close the US/ROK/Australia were to a major conventional war with NK at the end of 2010, and yet SK opinion on the street would tell you everything's relatively fine), the tension and lack of patience for NK very much exists and continues to build in the ROK gov/mil leadership. (for what it's worth, even though US is technically in administrative control of the ROK military, Obama more or less said he will go with what ROK administrations think is best for their country short of a completely unprovoked invasion or something)
Going back to the nuke thing and threats... like I said, there won't be an invasion tomorrow to put an end to this. However, I do think there is a trigger point for SK and Japan: a nuclear warhead demonstrated on a working ballistic missile.
In the bigger picture, though, this does have a few other ramifications. The markets are obviously too volatile to worry about their neighbor shaking things up again. China will lean harder than usual. Russia finds common ground with the West on the Korea issue (the only difference is that they hope a post-unification ROK doesnt have US forces haha), and will probably highlight cooperation in this (as well as Syria) to off-the-record petition for sanctions to be removed (esp with Donbass in a weird state). More interesting to me, though, is how Obama will treat this, considering it his last year. Will he seek olive branches, a harder stance, or more of the same US reaction in order to best set up the foreign policy climate for his preferred successor?