At the end of The Lord of the Rings, Frodo had a rather easy path through Mordor on his way to Mount Doom. And a casual observer might question why Sauron -- who was arguably the strongest being left in Middle-earth -- would leave a place as important as the Sammath Naur unguarded when he knew that the One Ring could be destroyed there. Well, to answer that question, one must at things from Sauron’s perspective, and upon doing so, it becomes clear that he thought that the fate of Middle-earth would be decided in from of the Black Gate when Aragon challenged him.
In trying to understand why Sauron emptied Mordor to accept Aragorn’s challenge, it's important to abandon all knowledge of Frodo’s quest. Sauron only knew what he could see with his eye or what he was told through the mouths of his spies, and by looking at it through that lens, it becomes clear that Sauron believed Aragorn had his ring.
Because of the Nazgul, Sauron knew that a group of hobbits set out from the Shire with a Baggins carrying the One Ring and were sheltered in Rivendell by Elrond. Assuming that the Elves’ goal would be to send the One Ring to Gondor as a way to win the war, he sent Saruman’s forces to confiscate it before they could reach Minas Tirith. And, as far as Sauron knew, everything was right on schedule when Pippin looked into Saruman’s Palantir.
Sauron’s first thought when he was Pippen would've been that Saruman was successful in capturing the Ringbearer, and he made him look into the seeing stone as a form of torture. Only later did the Dark Lord learn that Isengard had fallen and that Gandalf and Aragorn were involved. Thinking that one of them probably took his ring, he returned to his earlier train of thought -- everyone’s goal was to get the One Ring to the front line so it could be used as a weapon against him. His response was then to destroy the last fixture of Gondor in Middle-earth, and he attacked it with all haste.
Unfortunately, his forces were promptly defeated. Losing with such an advantage made Sauron suspicious, and the natural line of thought was that Aragorn or Gandalf had used the One Ring to defeat his vast army. Soon after, Aragorn looked into the Palantir and announced himself as the Heir of Elendil. This was a challenge to the Dark Lord, and when Aragorn dared to march on the Black Gate, Sauron was convinced that the Lord of Gondor was wielding the One Ring.
The only logical course of action for Sauron was to empty Mordor in a last-ditch effort to get his ring back. However, as most are aware, the whole thing was a ruse. Aragorn never had the ring because Frodo was busy sneaking in the back door to destroy it. In the end, it was a twisted bit of fate that ultimately destroyed Sauron. He made all of the races of Middle-earth subservient by preying on their lust for power and giving them rings. However, it was his own desire to regain power that led to his downfall.