If they manage to get it working as designed, it would radically change the economics of going to space. You can imagine the savings from not having to rebuild your vehicle after every use.
This would be a paradigm-shift and would likely cause a massive boom in human space activity. Space tourism and in-orbit manufacturing are two commonly discussed use cases that would become far more economical. Existing use cases such as remote sensing and communication would expand.
All this could cause positive feedback loops of innovation, cost reduction, induced demand, and so on. A new era of human space activity. That's what all the hubbub is about.
P.S. Not to mention the slightly more far-fetched possibility of human settlements on Mars…