An allusion is a brief or casual reference to some famous person (real or fictional), quotation, work of art, or other such well-known thing.
In this speech, the allusions are mainly taken from the Bible, but there is also one from classical literature/mythology.
Some allusions in this speech (in order)
Song of the siren -- from the women who tried to tempt Odysseus and his crew to their doom.
Having eyes, see not... -- Mark 8:18
Lamp to guide my feet -- Psalm 119:105
Betrayed with a kiss -- Refers to how Judas betrayed Jesus by kissing him
Battle to the strong -- Ecclesiastes 9:11
For more explanation about allusions, check out this video:
Allusions are especially common in persuasive writing because the author may attempt to refer to an event from the past that most likely correlates in some way to the topic on which he is speaking. Allusions could also be seen as ethical appeals because it adds to the credibility of the author in that he is well informed of important events or historical/literary texts. In Patrick Henry's "Speech to the Virginia Convention" he adds allusions at a few points to help nail his point.
One example is when he says, "We are apt to shut out eyes against a painful truth, and listen to the song of that siren, til she transforms us into beasts." This is an allusion to the Greek myth in which seductive sea maidens known as sirens lure sailors to a rocky shore using their beautiful voices and then turn the men into pigs.
Another example of an allusion is when he mentioned the new tax laws that the First Continental Congress had protested against. He says, "Is it that insidious smile with which our petition has been lately received?" King George did withdraw the tax with some conditions after the protest, but the colonists were not happy with these conditions. Henry is drawing a parallel with this previous political event.
It is especially interesting to study Patrick Henry's use of allusions because his final line "Give me liberty, or give me death!" became a very famous and frequently used allusion after his speech.
Patrick Henry's fiery and dynamic speech against the reviled Stamp Act, by which the British Parliament instituted taxes on all newspapers and public documents, set him apart as a man of dynamic locution. Furthermore, his address to the Virginia Convention in 1775 certainly has gained him historical recognition. This speech was one made as Americans came near the breaking point as Britain furthered its taxes and made other harsh measures, referred to as the Intolerable Acts. His speech contains several allusions, or references to other known works.
In addition to those mentioned, in the first paragraph, Patrick alludes to God as the "majesty of heaven, which I revere above all earthly kings." He later suggests "an appeal to arms and to the God of Hosts." This allusion is to Psalm 84:3:
Yea, the sparrow hath found an house, and the swallow a nest for herself, where she may lay her young, even thine altars, O LORD of hosts, my King, and my God.
Song of the siren
Betrayed with a kiss