King Richard I is a real, historical guy. He ruled England from 1189 to 1199 and led the Third Crusade of Christian knights to the Middle East to fight against the Muslims holding Palestine. He spent most of his life at war with various people – the French, the peoples of the Middle East, his own dad. With all this fighting, King Richard built up a reputation for chivalry – for living according to the honor codes of medieval knighthood – that has lasted for over eight centuries. (You can read more about the real Richard here.)
As a character in Ivanhoe, it's almost as if King Richard is two different people. There is that historical King Richard, the one we just described, who draws Ivanhoe out of England to fight by his side in the Crusades. That King Richard doesn't appear much in the book, because he's being held captive in Germany and then making his way back to England. (This really happened; he was held for ransom by Leopold V of Austria.) It's the absence of that King Richard that makes Ivanhoe possible, since it frees up his brother, Prince John, to bully the Saxons and generally make things more difficult for Ivanhoe and his family.
King Richard's other face in the novel is that of the Black Knight. That guy loves jests and drinking songs and hanging around with jokers like Wamba and Friar Tuck. He doesn't always take a lot of initiative against the Normans, which is how he gets his other nickname, the Black Sluggard ("sluggard" means "lazy person"). For example, at the tournament at Ashby-de-la-Zouche, he doesn't really participate until he sees Ivanhoe about to get killed in a three-on-one fight with Athelstane, Reginald Front-de-Boeuf, and Brian de Bois-Guilbert.
Still, when the Black Knight does jump into a fight, his mighty arm seems invincible. He knocks both Athelstane and Front-de-Boeuf out with no problem at the tournament. Later, when he joins the outlaws of Sherwood to storm Torquilstone, he's the one who fatally wounds Front-de-Boeuf in hand-to-hand combat. As Rebecca comments, "it is fearful, yet magnificent, to behold how the arm and heart of one man can triumph over hundreds" (29.58). This is a guy who knows how to kick back and have a good time, but he's also ready to battle evil one-on-one when he sees it.
So we have this division in Ivanhoe between historical King Richard, always away from his kingdom fighting, and the novel's King Richard, who enjoys going out among the people, saving damsels, and doing good deeds. King Richard's split personality is important to his characterization. The thing is, King Richard is a legend; he's one of England's great symbols of kingliness and medieval knighthood. But... he only spent six months out of his ten-year reign actually in the country! (source). Think about that for a second: that's 5% of his reign. If the President of the United States spent 5% of his four-year term (less than three months) physically in the US, there would be a national panic. Even though Richard was supposed to be ruling England, he clearly cared more about fighting and warfare abroad than domestic issues.
Scott points outright to this conflict between our ideal of the heroic King Richard and the reality of his poor performance on the home front. When Richard tells the outlaws of Sherwood his true identity, he settles in for a long party with the guys. He doesn't want to take back his throne and responsibilities as king. It takes the encouragement of Locksley (Robin Hood) and Ivanhoe for King Richard I to get a move on and put down his brother John's rebellion. Scott describes him this way:
Novelty in society and adventure were the zest of life to Richard Coeur-de-Lion, and it had its highest relish when enhanced by dangers encountered and surmounted. In the lion-hearted King, the brilliant, but useless character, of a knight of romance, was in a great measure realized and revived; and the personal glory which he acquired by his own deeds of arms, was far more dear to his excited imagination, than that which a course of policy and wisdom would have spread around his government. Accordingly, his reign was like the course of a brilliant and rapid meteor, which shoots along the face of Heaven, shedding around an unnecessary and portentous light, which is instantly swallowed up by universal darkness; his feats of chivalry furnishing themes for bards and minstrels, but affording none of those solid benefits to his country on which history loves to pause, and hold up as an example to posterity. (41.14)
In other words, King Richard I was the kind of glorious, brave guy that people love to sing about, but he didn't actually do very much to improve life in England. Scott brings out the side of Richard that makes for great stories – the side that loves daring deeds and mortal combat. But Scott can't deny that the historical King Richard was not a great leader. He makes a better romantic hero than a real-life king. No wonder the character of the Black Knight spends so much time singing songs with Wamba and Friar Tuck. King Richard I always comes off better in ballads and legends than he does in history books.