Khal Drogo is the leader (khal) of a very big army/tribe (khalasar). He marries Daenerys, makes her happy for a while, and then dies.
He's a Dude
Khal Drogo is a stud. Yep, that's right. He's never had his hair cut, which means that he's never lost a battle. (That's what Dothraki do: they put bells in their hair for victories they win and cut off their hair when they lose.) The very first thing we hear about Drogo is that even his slaves wear gold (4 Daenerys 1.22), which either means he doesn't like gold or he has a lot of it. (He has a lot of it.)
And a Good Husband, To Boot
Drogo is not only powerful, but surprisingly gentle (which is particularly appreciated during Daenerys' first time having sex [12 Daenerys 2.62]). Even though Drogo and Daenerys' is an arranged marriage (arranged by the greedy Illyrio Mopatis and Daenerys' snaky brother Viserys), it turns out to be a great match for both of them.
In fact, Drogo is so great that it seems perfectly natural for Daenerys to align herself with her Dothraki husband rather than her brother, the jerk from Westeros. (Although, to be fair, Drogo would make any man look bad by comparison, not just a whining bully like Viserys.) So Drogo may be here to help Daenerys grow both in her capabilities (she becomes stronger and more confident from her marriage) and in her interests (Daenerys starts to feel more at home with the Dothraki than with Viserys' tales of the Seven Kingdoms).
Good as Dead
Drogo has one more function in the story: to try to give Dany what she wants and, well, to die trying. Once Drogo helped Daenerys grow into the role of khaleesi, he would just hold her back, right? Now that he's dead, who knows what Daenerys will become in the next books.
Despite the crazy number of characters in A Game of Thrones, George R.R. Martin gives us some helpful tools to keep track. And here's one of them: doesn't the title "khal" sound kind of like "khan," as in Genghis Khan? In this way, Martin helps us make a connection between a real historical figure (Genghis Khan and his horde of horse-riding conquerors) and a character in his invented history (Khal Drogo and his khalasar of horse-riding conquerors). Thanks for the tip!
Minor Characters Connected to Khal Drogo
Cohollo, Haggo, Qotho: the Khal's Bloodriders
Bloodriders are a type of bodyguard for the khal, but they're sworn to him at his birth. And at his death, if they are still alive, they would kill themselves to join him (after killing whoever killed the khal, of course). This is a pretty radical form of service they provide, which we could compare to the Kingsguard of the Seven Kingdoms. Unlike the Kingsguard, which includes oathbreakers like Jaime Lannister, the bloodriders are true to their oaths.