Clearer terms are "overhead" and "programs". Overhead includes salaries, fundraising, marketing, general expenses, etc. Program spend is how much they spend on programs from the stated mission. Providing nets would fall into the latter category.

But I don't want nets, I want people to be helped by nets and that requires a lot of work. So the efficiency of a charity is a way of saying that if you give $10, that means $10*efficiency nets in hands of people that need them.

Although I partially agree with you, it is easy to show why your reasoning doesn't work. Let's say I create a charity to provide nets. I pay myself 99.99% of all donations and use the rest to fly somewhere myself and hand over 10 nets so I get a free vacation as well. And this is not a wholly theoretical discussion, I am sure there has been a charity like this.