Explain how fossils of birds similar to modern birds provide evidence of climates in the past.

By analogy. the idea is that bird forms reflect the environment in which they live. the environment includes climate or rather perhaps climate is a very big influence on the environment. If you have birds that have the features of tree seed eaters, that indicates a forested environment, if they are bug eaters, then there are bugs to eat, and so on. Animals tend to "fit" in their living space. If they don't, they move or die. So when we see fossils with certain features, we conclude that they have those features because they are living in an environment that is similar to the environments inhabited by existing life with similar features.