One of the fascinating elements of the History plays is the way in which they intersect with actual history. It is key to have some knowledge of the rather messy and bloody history of the crown in England in order to answer your question. Let us remember that King Henry IV gained the throne through rather nefarious means: he deposed and murdered the king that came before him, Richard II. Therefore, when the play opens, we see a man who appears to be wracked by guilt and upon whom the crown sits very heavily. Note the opening words of the play and how they emphasise this impression of his character:
So shaken as we are, so wan with care,
Find we a time for frighted peace to pant
And breathe short-winded accents of new broils
To be commenced in strands afar remote.
Note how Henry describes himself as being "shaken" and "wan" with the responsibilities of the throne. The alliteration of the "p" sound in the second line emphasises the way that the current peace he enjoys is only viewed by him as a chance to swiftly draw breath before the "new broils" descend upon him. He is therefore a man who, having achieved what he wanted, appears to be weighted down with guilt and with the realities of being king. Note how he mentions the desire to go on a pilgrimage to atone for his rather bloody assumption of the crown.