"General welfare" means a welfare - well-being of an entire population, or of a majority of a population.
Education generally helps in a welfare - it opens new job opportunities, thus limiting or eradicating poverty, and it helps in making better personal decisions, for example to buy fresh food and self-prepare it, which can be healthier and cheaper than buying at restaurants.
So education, improves people's lives, and a widespread access to education will improve people's lives in a majority of a society