That's because each ring corresponds to a year of growth, and good years with favorable temperature and precipitation correspond to relatively large rings. To use tree ring data, scientists have to have trees. They can look at tree rings from trees recently cut down, or they can use a bore to study rings from live trees without cutting them down. They can also use long dead trees from ancient structures or shipwrecks. Wood that has been well preserved over the centuries works particularly well.
Pollen can provide very good evidence of what regional climate was like for a given area.
To find pollen that corresponds with ancient times, scientists take cores from lakes and sediments. For every species of pollen, there is a suite of habitat conditions that would have been necessary for that species to survive and thrive. So if certain pollen grains turn up in a sample, scientists can make accurate predictions about what regional climate conditions were probably like at the time. Like pollen, other species of organism can yield clues to scientists about ancient climate patterns. The same is true for marine animals.