This translates as “generous heart.” Anyone that fails to show nam jai is looked down upon in Thai society. When you read on Thai girls’ dating profiles that they are looking for a generous man, they mean a man that has nam jai. It is not just about handing out all your cash to all and sundry, and it’s also nothing to do with taking advantage of your good nature either, although there are opportunists out there.
In rural communities in particular, most people don’t have many worldly goods, but most people no matter how poor will happily share what they have with you as it is a way of expressing their nam jai. Since you are likely to have more money, you’ll be given lots of opportunities to spread the wealth. This might be exactly what a Thai person would want to do, but it might not be your idea of a good time!