Your soft skills are your people skills. How well you handle difficult situations at work. How well you get along with people at work. How well you work in a team. How well you manage people. And how well you manage your life. So they, obviously, are very important.
Your hard skills are those skills you acquire by going to school, reading technical books and doing certification courses. They determine what you can do but don't care so much how you make people feel while doing it. And they are the bulk of what we list in our resume and CV.
So why do I say hard skills are more important than soft skills?
First, we live in a hard world. When it comes to low level jobs, we always prefer the candidate with the best soft skill. Everyone wants a house-help with more soft skills than hard skills. You care more about how she addresses you, get along with people and handle difficult situations than any housecleaning certificates she has. And when we move up to a higher level job, we want almost an equal mix of soft skills and hard skills. That is why most last stage job interviews focus more on how well you will fit into their company culture and get along with your new colleagues. But when we move up higher still, we get to a stage where we only care if you can do the job and not how you do the job.
When a country is looking for a bomb expert they don't care if he is bipolar or not. When a company is dying and needs a saviour, they hire someone with the hard skill of turning around businesses even if he is heartless. When we want the best and guaranteed results we always go (and pay very high) for hard skills over soft skills.
And then on a personal basis, there is a natural limitation to the wealth of soft skills you can acquire which we almost always quickly reach. If you are unfortunate to be on same level of people skills as I am, then all the learning and schooling in this world can't help you much, soft skills wise. But if you were born a politician and have all the charisma God could stuff in one person, no one is going to pay you enough to make you a millionaire just because of of your soft skill. To make any substantial earning you will need some in-demand hard skills. But without any soft skill and just some high-end hard skills you can live like a king. Though it could be better if you had soft skills, still, it would be impossible if you had just soft skills.