The calving itself will simply be the birth of another big iceberg. But there is valid concern among scientists that the entire Larsen C ice shelf could become unstable, and eventually break up entirely, with knock-on effects that could take decades to play out.
Ice shelves essentially act as corks in a bottle. Glaciers flow from land towards the sea, and their ice is eventually absorbed into the ice shelf. Removal of the ice shelf causes glaciers to flow faster, increasing the rate at which ice moves from the land into the sea. This has a much larger effect on sea level than iceberg calving does.
Basicly, take out the cork, and all the ice flows down into the sea, raising sea levels due to buoyancy (and then eventual melting). In the case of Larsen C, that would raise sea level by 10 cm over a decade or two. Which doesn't sound like much, but the problem is that Larsen C is only one (smallish) ice-shelf. I'm currently reading Kim Stanley Robinson's New York 2140, which is set in a future where climate change continues and a whole bunch of them go. And the result is 15 metres of sea level rise in a couple of decades - which is enough to trash every coastal city in the world, put entire countries underwater, and cause hundreds of millions of people to become refugees. And that's... not going to be pleasant. Just on a local scale, it means the CBD's of Wellington, Christchurch, Dunedin, and half of Auckland will be under water. You can imagine the disruption that would cause.
If we want to avoid this, the world needs to decarbonise quickly, and we need to do our bit. But our government simply doesn't seem interested in that. Which means we need to replace them with one that is - and the sooner, the better.