The Khan's impression of Marco's description of his desert

As for you merchants you crossed ocean and mountain the great Takla Makan Desert. One not many men survive. Describe for me my desert, hmm?

I can think of three possibilities, which repeat in a subsequent scene, probably with similar motivations:

1. Basic curiosity and information gathering for the court -- the Mongolian Empire was so vast that he may never have personally been so far West (the journey would take 3 years each way).

2. A test of their respect for his empire and their gratitude for his gracious license to open trade deals on his Silkroad -- when Marco's father and uncle described his desert, his land, his empire, as a "sea of death," the Great Khan was visibly irritated. Marco recognized this and quickly launched into a poetic, favorable description.

3. To assess the merchants' intelligence -- based on Marco's eloquence, Lord Kublai complimented him, says he has a "clever mind".

After Marco is secured, he is asked again:

When you and your father crossed Central Asia you passed through Badakhshãân. Describe for me, in the way that you do how you made the passage, what you saw.

1. Kublai is snacking on the throne, and possibly desired some entertainment and distraction from his worries by satisfying his curiosities.

2. A test of his new subject's powers of perception -- he intended to use Marco to gather intelligence from an objective source; we hear the recurring phrase, "Report to me what you saw as you saw it"), as he knew his courtiers didn't always paint an accurate picture.

3. A way to ascertain whether Marco was now going to show respect, another test he almost failed -- and in a way, Marco was testing Kublai, too -- but he instantly acquiesces following the order to "stuff his mouth with the shit of pigs." If Marco thought he would be set free if he acted impudently, he immediately realizes his miscalculation.