Paleontology is the branch of science dealing with study of past life. Paleontologists are the scientists that carry out this study.
The study of past life is done through the study of fossils which are evidence of that past life. Fossils may be the remains of organisms (plants, animals, etc.) or the remains of their activities (footprints, burrows, etc.). The later are called trace fossils.
Paleontology covers the entire span of life on Earth, from the first organisms around 4 billion years ago, up to the present day. However, scientists which study recent human activity, the last 12,000 years or so, are generally called archaeologists, and their study is called archaeology. There is a blurry line where archaeology begins and paleontology leaves off.
Paleontology is generally considered a part of geology, though because it involves life, it can also be considered a part of biology. Paleontologists must know something of both geology and biology. In particular in geology they must understand sedimentary geology - the study of sediments. In biology paleontologists need to know something about comparative anatomy, and in particular the anatomy of the organisms they study.
There are many sub-groups within paleontology, depending on what specifically is being studied. Among these is Vertebrate Paleontology (the study of fossil animals with backbones), Invertebrate Paleontology (the study of animals without backbones), Paleobotany (the study of fossil plants), and Paleoecology (the study of ancient environments). Almost everything within paleontology has it's own specialist name.