Deuteronomy is so called from the Greek name for the Book. "deuteros" meaning second, "nomos" meaning law, because Moses rehearsed the Law for a second time, before the Israelites entered the Promised Land.
Deuteronomy contains three speeches by Moses (Deut. 1:6-4:40, chapters 5-26, and chapters 29-30) in which he remiinds the people of God's love towards them, and His mighty acts in bringing them out of slavery. He goes on to remind them of the Laws which God has given them, and warns them of the temptations they will face as they meet people who worship other gods and goddesses and whose ways are often cruel and immoral.
Chapters 31-34 continue the account in the Book of Numbers of the preparations to enter the Promised Land.

Deuteronomy 1:11 - "On this side Jordan" refers to the East side of the river Jordan
Deuteronomy 1:3 - "in the fortieth year, in the eleventh month, on the first day of the month" indicates the time elapsed since the crossing of the Red Sea.
Deuteronomy 2:4 - the "Children of Esau" were the Edomites, descended from Esau the twin brother of Jacob. Their territory included the mountainous region to the south and east of the Dead Sea. Their capital was Petra, a city hidden in the mountains and approached only by a long narrow gorge.
Deuteronomy 2:8 - Ezion-Geber (now also called Eilat) : the region on the northern tip of the Gulf of Aqaba. Famous for deposits of iron ore (mined from the time of Solomon onwards) and a blue-green semi-precious stone 'the stone of Eilat', a blend of lapiz lazuli and malachite. Now a major resort and center for scuba-diving.
Deuteronomy 2:9 - the Moabites were descendents of Moab, the son of Lot and his elder daughter, Genesis 19:30-38. The Mountains of Moab overlook the eastern coast of the Dead Sea
Deuteronomy 2:19 - the Ammonites were the descendents of Ben-Ammi, the son of Lot and his younger daughter, Genesis 19:30-38. The name is still used for the capital of Hashemite Kingdom of Jordan, Amman.
Deuteronomy 3:1 - Bashan was the region to the east of the Sea of Galilee. There was enough rainfall there for good pasture for cattle, so the half-tribe of Manasseh settled there rather than in the Promised Land. In later times the Israelites who lived in Bashan became rich and self-satisfied, and were denounced by some of the prophets for turning away from God (eg. Amos 4:1)
Deuteronomy 3:11 - Og, king of Bashan, had a bedstead of iron - the time is towards the end of the Bronze Age. Iron-working was beginning to be known, but weapons and armour were still mainly made of bronze. At that time an iron bed-stead was probably more rare and valuable than one made of gold.
Deuteronomy 3:12-13 - Gilead was the region to the south of Lake Galilee, on the east bank of the Jordan. It was fertile, and had enough rainfall to grow good grass for cattle
Deuteronomy, chapters 4 - 33 - The time was roughly 40 years since the giving of the Law at Mount Sinai (also called Horeb), so Moses reminded the new generation of Israelites of what God required of them
Deuteronomy 11:18 - "bind them for a sign upon your hand, that they may be as frontlets between your eyes" - to this day, when devout Jews pray they bind little boxes (phylacteries) containing scripture verses on their right arms and on their foreheads
Deuteronomy 11:20 - "write them upon the door-posts of thine house" - this is still done in jewish homes, and even on each Jewish hotel room in Israel : a small box, often ornately decorated, containing a parchment with a scripture verse, is attached to the door frame. This is called a "Mezuzah" (meh-ZOO-zah, plural Mezuzoth)
Deuteronomy 12:16, 12:23-25 - to this day, for meat to be kosher (ritually clean, suitable for eating) the animal must have been killed and bled by a trained and certified butcher
Deuteronomy 19:1-13 - see Numbers 35:12
Deuteronomy 25:13 - "thou shalt not have in thy bag diverse weights" i.e. have a heavy one for buying things with and a lighter one for selling them
Deuteronomy 26:5-9 - "A Syrian ready to perish . . . " often quoted as "A wanderiang Aramean was my father . . " these verses represent one of the earliest confessions of faith for the Israelites, as they sum up the events of Abraham's call, the slavery in Egypt, and the Exodus
Deuteronomy 27:12-13 - Mount Gerizim and Mount Ebal, the Mount of Blessing and the Mount of Cursing - these two mountains face each other across the valley where Shechem is now situated. Mount Gerizim is green with grass and trees, while Mount Ebal is rocky and infertile. The Samaritans still use Mount Gerizim as the center of their religious rites.