Mordor was surrounded by mountain ranges: the Ered Lithui (Sindarin: Mountains of Ash) from the north, the Ephel Dúath (Sindarin: Mountains of Shadow) from the west, and in the south. In the northwest corner there was the valley of Udûn, and the Morannon (or Black Gate) which was the way into Mordor. Near the foot of the Ered Lithui lay Barad-dûr (Black Speech: Lugbúrz), Sauron's fortress from where he ruled over his lands. South of Barad-dûr lay the region Gorgoroth, in the middle of which stood the volcanic mountain Mount Doom, where the One Ring was forged and the only place it could be destroyed.
Through the Ephel Dúath led the pass of Cirith Ungol, guarded by th Tower of Cirith Ungol. Cirith Ungol was inhabited by the great spider Shelob. Minas Morgul was a city built in Ithilien, the former Minas Ithil. It was commanded by the Witch-king of Angmar, leader of the Nazgûl. Further south lay the inland Sea of Núrnen and Núrn the southern part of Mordor. This area was more fertile, in part due to the volcanic ash; it was used as farmland to feed Sauron's forces, worked by his servants and human slaves.
Mordor was mostly populated by orcs who were also the staple of Sauron's army. There were also a significant number of trolls, the Nazgûl, The Mouth of Sauron (who acted as ambassador to an army of attacking forces from Gondor and Rohan) also lived in Mordor.
Sauron's defeat was when Isildur and others lead a force of men and elves to combat Mordor's forces. Sauron had a ring which gave him incredible power. Isulder was able to steal the ring from him in battle and Mordor's forces were defeated.
Osgiliath was a key city in the later war between Mordor and Gondor. Mordor had to win the city if they were ever going to defeat Gondor. The general of Gondor's army, Boromir, destroyed the bridges over the River Anduin to temporarily halt Mordor forces. Defense of the city was left to Captain Faramir after Boromir left and he was able to hold the city for a little while. Mordor eventually overwhelmed them with numbers and the city was taken.
After taking Osgiliath; Mordor sent a massive force of trolls, orcs and allies from the southern nations to take the city of Minas Tirith; the capital of Gondor. Minas Tirith was protected by large walls spread out over the Pelennor Fields. Gondor's were outnumbered more than ten to one. Mordor advanced through the field breaching the walls with siege engines. Gondor was forced to retreat steadily back toward the city. When Mordor reached the city they used a battering ram named Grond to breach the main gate. The Lord of the Nazgûl entered the city but was stopped by Gandalf the White. Before Mordor could enter the city they attacked by a large army of Rider of Rohan. Rohan and Gondor were still heavily outnumbered, and Rohan's king Theoden was killed by the Lord of the Nazgul (who was killed soon after by Éowyn and Merry). Theoden's nephew; Eomer took command and lead Rohan to defeat the Southrons (allies of Mordor). A force of men from Southern Gondor arrived under the command of Aragorn. Together Rohan and Gondor were able to defeat the Mordor army.
After saving Minas Tirith; Rohan and Gondor lead a small force to the Black gate to attack Mordor. There plan was to distract Sauron so that he would not find Frodo. Frodo was in Mordor attempting to destroy Sauron's ring in Mount Doom. If he did this Sauron would be defeated and Mordor's forces would crumble. After a small dialogue with Sauron's ambassador (who lead them to believe that Frodo had been captured) Mordor forces trapped them. Rohan and Gondor were outnumbered again but they stood their ground. The eagles came to join the fight. Frodo eventually destroyed the ring and Sauron and Mordor were defeated forever.