Henry stresses that the men have a choice: they are free men and do not fight because they are compelled to do so:

That he which hath no stomach to this fight,

Let him depart; his passport shall be made

And crowns for convoy put into his purse:

We would not die in that man's company

That fears his fellowship to die with us (IV.3).

Even during Shakespeare's time, the idea of fighting for freedom was clearly a compelling rhetorical strategy. On the surface, fighting for a piece of land might not seem to be a noble quest when done purely for the purposes of enriching the crown. This is why Henry's speech is so perfectly analogous to a speech made by a CEO or another business leader: often, quite cynically, shareholders and employees will assume that decisions are made for personal profit, not to advance the common good. Although the actual cause might be dubious, Henry gives it a moral foundation. Just like in Pericles' funeral oration, which praised the Athenian people for their democracy as well as their valor, Henry gives the English troops a moral reason to fight the more aristocratic French.

Henry is also capable of using a 'personal touch' in his rhetoric that shows he cares about his men. Of course, Henry does not know the personal name of every single soldier in the English army, but he does his best to honor the names of those whom he does know: "Harry the king, Bedford and Exeter, Warwick and Talbot, Salisbury and Gloucester." He speaks of himself as "Harry" in a familiar sense and in the same breath as lower-born men.

These types of rhetorical flourishes are why Henry V, in contrast to his predecessors, was known for his astute emotional intelligence as a leader. Instead of holding himself above the common people, he was...

Only because Henry speaks to his men in an earlier scene, the night before the battle, can he know how his men 'tick' and carefully find the phrases to make them want to fight and overcome the odds. Even though he had a profound sense of the unique responsibilities of kingship, Henry is also willing to open up his ear to the concern of everyday soldiers, and tailor his speech to their perspective on the ground.
Henry has 'head, heart, and guts' when leading his men in battle. Although his decision to embark upon a war may be rash, as he matures as a leader he becomes more capable of using tactical strategy and his charismatic power to succeed. He is able to take a fresh perspective and to reframe his quest for land in a manner that transcends his own persona and makes it an English quest, not a personal quest. Yet even though he claims that the cause has nothing to do with his own ego, it is only because of his ego and magnetism that such a transformational approach is effective. He does not create false expectations for leadership, but demands that his men live up to his example.

Henry makes it appear he goes above and beyond what is required for a leader, and in many ways he does -- he fights side-by-side his men, rather than commands from a distance. He uses effective public relations 'market research' before making his Crispin's Day appeal, when he spends the night with the common soldiers. Henry swears that the king will fight to the death, just like his men, and not allow himself to be 'ransomed' by the enemy. By vowing to be die beside the lowest of the low, Henry achieves one of the greatest of victories in English history.

References

Freiberg, Kevin & Jackie Freiberg. (2003). Guts! Doubleday.