There’s an intuitive difference between telling you to "close the window" and saying that "the window is closed." In saying that the window is now shut, I'm trying to describe the way that the world is. But when I issue commands, I'm not telling you about what the world is like. I'm trying to get you to change what the world is like— to bring about a certain state of affairs. We call this the world-to-word direction of fit (the world must be made to match the words). Promises are also like this. When I promise you that I’ll come to your play, I am changing the world by taking on an obligation. I have to do something to match my words— in this case, go to your play. Promises and desires are different from many everyday assertions. When I report that the window is closed, I’m trying to do the opposite kind of thing. I’m trying to get my words to match the way the world already is; my statement is an example of the word-to-world direction of fit (the words must be made to match the world).
People often use direction of fit to talk about the difference between wanting something and believing something. When I want to be a painter, I want the world to change to fit my desires. I'm not a painter right now, but I want the world to change into one where I am a painter. And, even if I don't ever become a painter, we don't think that my wanting to be a painter is a bad thing. Wanting to be a painter is an instance of the the world-to-mind direction of fit (the world must be changed to match what’s going on inside my head). This is really different from beliefs. If I believe I am a painter, but I have never held a paintbrush, there's a problem. When we believe things, we want them to be true about the world. Our beliefs are supposed to match the way that things are-- and believing that you are a painter when you are not one is bad in a way that wanting to be a painter when you are not one isn't. My beliefs exhibit the mind-to-world direction of fit (my beliefs have to match the way things are in the world).
Direction of fit is also relevant to debates about morality. Some people think that when you make moral claims like "eating meat is wrong", you’re really expressing your attitude towards meat eating instead of describing the way that things are. On this view, our moral beliefs are a lot like desires: when we say that "eating meat is wrong", we really want the world to change to match our negative-attitude towards meat eating. Morality, on these views, is world-to-mind. Other people, however, think that moral claims are not like this. They hold that the direction of fit works the other way. When we make claims like "eating meat is wrong", we are taking our beliefs to match things as they already are in the world— there is a fact that eating meat is wrong, and we are just trying to match our beliefs to the way that the facts are (mind-to-world direction of fit).