Archeology is a scientific discipline concentrating on reconstructing human cultural histories before recorded civilization. By studying those few artifacts (pottery, stone structures, bone tools, etc.) that have survived centuries of destruction, and by taking the clues they offer, reimagining the lives of people as they were lived before formal recorded history, archeologists tell modern man much about his origins, his development as a thinking societal species. Usually separated from paleontology (the study of bones and human remains in graves, etc.), it is considered both a hard science and a sociology discipline. It uses deductive reasoning to flesh out a full picture from fragments, and inductive reasoning to make working assumptions about what is not known from solid evidence. The reconstruction of Troy, whose remains were discovered by Schliemann, is a landmark archeology mapping project, as are the remains of cities buried by the eruption of Pompeii. These reconstructions told us much about how our ancestors lived.
I also guess that we could simply say that archaeologists basically study the past, history via its artefacts, remains, the 'physical evidence' of the earlier times/people/civilizations.
Archeologists dig for clues to study the distance past. The most famous fictional archeologist, Indiana Jones, was always looking for relics to discover what the past was like. Real archeologists do the same thing, but without the gun fights and chases.