The sun has always been a common symbol for kings and queens who liked to give themselves props for their stunning powers. (Ever heard of Louis XIV of France, a.k.a. the "Sun King"? Enough said.)
Throughout this play, Shakespeare aligns King Henry V with the sun. As it turns out, Shakespeare's been developing this idea since Henry IV Part 1, when Henry (a.k.a. Hal) uses the sun as a metaphor for his promised transformation from a wild young prince into a majestic monarch:
Yet herein will I imitate the sun,
Who doth permit the base contagious clouds
To smother up his beauty from the world,
That, when he please again to be himself,
Being wanted, he may be more wonder'd at,
By breaking through the foul and ugly mists
Of vapours that did seem to strangle him. (Henry IV, Part 1, 1.2.29)
Here, Hal (who's been acting like a total punk lately) promises that he's going to throw off his bad behavior like the sun breaks through the "foul and ugly mists." The idea is that we'll all be dazzled by his glorious transformation into a capable monarch.
Even though Henry later makes good on his promise, the Dauphin of France refuses to recognize his transformation (which is why he sends him a chest full of tennis balls to play with). Henry's response to the insulting gift follows:
But I will rise there with so full a glory
That I will dazzle all the eyes of France,
Yea, strike the Dauphin blind to look on us. (Henry V, 1.2.10)
Later on, the Chorus uses the same metaphor to describe Henry's warmth and strength as a leader. As Henry moves through the English camp cheering up his frightened troops, the Chorus compares him to a sun that "thaws" his men's "cold fear":
With cheerful semblance and sweet majesty;
That every wretch, pining and pale before,
Beholding him, plucks comfort from his looks:
A largess universal like the sun
His liberal eye doth give to every one,
Thawing cold fear, that mean and gentle all. (Henry V, Act 4, Prologue)
So, basically, King Henry is kind of like an emotional microwave that's set on "defrost" mode.
P.S. We triple dog dare you to trace Shakespeare's use of "sun" imagery through the whole tetralogy, from Richard II through Henry V.