I have a recipe that calls for leaf gelatine but I have none. What does gelatine do in a recipe?
It really depends on how much of it you're using.
If it's only a small amount, it might be for mouthfeel -- it'll make the liquid more viscous and less 'watery'. Consider a good chicken soup, where the broth has a bit of body to it.
If it's a large amount, it's to get the liquid to set up. In something like a panna cotta, aspics, mousse, or a no-bake pie, it's to get the liquid to firm up and become either solid or at least scoopable.
And gelatin doesn't need to be used in solely liquid dishes -- America's Test Kitchen used in a meatloaf recipe for what was most likely mouthfeel.
... but it's possible that there are other uses. I seem to recall hearing that it can be used to clarify broths as well.