Fossil discoveries led to a number of important observations in the mid to late 1700's. First, an English geologist named William Smith (1769-1839) realized that certain fossils always showed up in the same kinds of rock, even if they were found in different locations around England. Moreover, both the fossils and the surrounding rock occurred in layers, and these layers usually stacked up in the same order no matter where they were found.
Stratigraphy—the study of layers of rocks and sediments—had been around for a while before Smith, but he was the first person to apply the principles of stratigraphy to the problem of dating layers. Smith realized that, if two different sites had the same rock layer containing the same fossils, they must come from the same time period! He called the predictable layering of fossils the Principle of Faunal Succession, because the animals (fauna) in the layers always occurred in the same order (succession). This principle was very useful, because it allowed people to correlate layers from different locations, and allowed them to figure out roughly how old a layer was even if surrounding layers were missing. Today, we can also date sediments directly using radiometric dating—check out "In the Real World: Biotechnology" to learn more.
Image from here.
A second important observation was that fossils in layers closest to the surface (and therefore, the youngest layers) most closely resembled living organisms, whereas fossils in lower, older layers of rock looked substantially different from living forms. Some of these organisms in older layers no longer existed on the planet—they had gone extinct! Extinction of a species occurs when all members of that species die. All these observations led to the undeniable conclusion that life had changed over time, and that some species had kicked the bucket, while others had sprung into existence. These ideas were inconsistent with the creation story, and provided strong support that evolution had occurred.
Fossils are also important because they show transitional forms. That is, they show intermediate stages as an organism evolves from one thing into another, or as one kind of organism diversifies into many kinds of organisms. Check out "In the Real World: Current Research" to learn about some of the cool transitional forms that have recently been discovered. These transitional fossils provide direct evidence that life forms change over long periods of time.