Bactria was an ancient region in central Asia, roughly bounded by the Oxus River and the Hindu Kush mountains to the north and east as well as China in the east, Persia in the west and India in the southeast. It first shows up in history as an eastern province of the Persian Empire, where it benefited and grew wealthy from the Siberian-Indian-Persian trade in metals and other goods. It was brought under Persian influence by Cyrus II around 530 B.C. Its satrap, Dadarshish, helped Darius I defeat an Armenian uprising as well as putting down resistance in the neighboring province of Margiana. Dadarshish was succeeded by Artabanus, who ruled from 500-465 B.C.
Masistes, a brother of the great Xerxes, had planned to start a revolt in Bactria in 480, but was killed before his rebellion could succeed and Bactria remained under Persian influence until Alexander the Great came along. When he faced Darius III at the battle of Gaugamela, Alexander marked out the Bactrians as being the strongest force of the Persian army. Alexander defeated Darius ultimately and Darius tried to flee to Bactria, but was killed by Bessus, its satrap and his relative. Bessus then assumed the throne of Persia.
Although Bessus resisted Alexander as much as possible, he was conquered and killed anyway. Alexander wintered in Bactra, the capital of Bactria, during the winter of 329-328 B.C. before moving on to conquer Sogdiana. Bactria immediately rebelled, but Alexander put that rebellion down as quickly and brutally as possible, taking about 30,000 Bactrians hostage. The region was made culturally Greek after his conquest where it had previously been more Persian. Alexander's conquest also partially severed ties with the Persian Empire, and set up a Greek state of which Bactria was theoretically part in the area under Seleuchos I, although Bactria would not be fully independent until 256 B.C. During this time, Bactria was probably very wealthy, although records for this period are apparently scarce. The new satrap, Diodotus I, declared independence from the Seleucids. They didn't try to reclaim it until 208, when they began a two year siege of Bactra to reclaim Bactria. They were thwarted by Bactria's second ruler, Euthydemus, who won out in the end.
His son and successor Demetrius made Bactria into a fairly powerful state. Antiochus IV, the Persian ruler of the Seleucids, sent Eucratidas to subjugate Bactria and Eucratidas killed Demetrius in 167 B.C. by raising a rebellion during which Eukratidas then established himself as the king of the "thousand cities of Bactria." He was then killed in 159 B.C. by his son Eukratidas II, who then siezed the throne.
After Demetrius's death, someone had to fill the power vacuum, and Demetrius's general Menander did just that until his death in 145 B.C. Bactria's rulers hadn't been able to set up a very strong state apparatus, and after Menander's death no one ruled the region at all until it was partially absorbed into the Kushan Empire in 130 B.C. and partially taken over by the Tocharians in 100 B.C. These latter had expelled the Saka, who had conquered Bactria forty years earlier. It did not change hands again until the fifth century C.E. when it was conquered by the Ephthalites, who then lost it to the Turks in the 6th. After that, it wasn't so often called Bactria.
Although it was culturally and administratively Greek for much of its existence, what was then called Bactria is near what is today northern Afghanistan. Its capital city, Bactra, sat in the same spot as Balkh in northern Afghanistan. If you want to see pictures of artifacts from Bactria when it was still called that, you can find a few at http://www.hp.uab.edu/image_archive/ucd/. I have no clue about physical anthropology, so I won't make a fool out of myself by trying to interpret what you can see for yourself more easily anyway.
Yay for spontaneous content rescues.