Patrick Henry uses a skillful combination of pathos (an appeal to an audience's emotions) and logos (persuasion by reason) in his famous speech to the Virginia Convention.
In terms of the former, Henry tries to play upon the other delegates' attachment to liberty to drive his point home. Henry will have known before making his speech that many members, if not most, of his audience would still have believed it was possible to reach an amicable settlement with the British. In order to convince them otherwise, Henry knew that he had to appeal to his audience's deepest emotions, not just to their heads but their hearts. The delegates to the Virginia Convention may have had their differences, but all of them were united by a passionate love of liberty, and it's that governing emotion that Henry sets out to exploit in his speech.
In practical terms, this means bolstering his argument by setting out a litany of grievances against the British, emphasizing certain key emotive phrases to make his point:
Our petitions have been slighted; our remonstrances have produced additional violence and insult; our supplications have been disregarded; and we have been spurned, with contempt, from the foot of the throne.
The message is clear and unmistakable. Despite their best efforts to find a peaceful solution, the American colonists have been rebuffed by the British at every turn. That being so, there's no alternative left but to stand and fight for the cause of liberty.