Pope’s poem is a mock-epic: that is, a poem that treats insignificant events in the manner of epic poetry. The opening couplet, which you quote, sets the stage for the entire poem, suggesting that the seizing of Belinda’s lock of hair (the “rape” referred to in the title of the poem) is a “trivial” event which nonetheless will inspire “mighty contests,” which the poem will record in true Homeric fashion. Pope knew Homer well—he made one of the great English translations of Homer. Compare Pope’s opening with the opening of his translation of the Iliad, for example:

Achilles' wrath, to Greece the direful spring

Of woes unnumber'd, heavenly goddess, sing!

That wrath which hurl'd to Pluto's gloomy reign

The souls of mighty chiefs untimely slain;

Whose limbs unburied on the naked shore,

Devouring dogs and hungry vultures tore.

Since great Achilles and Atrides strove,

Such was the sovereign doom, and such the will of Jove!

The quotation, 'What dire offense from amorous causes springs,/What mighty contests rise from trivial things' is the opening couplet of Alexander Pope's 'The Rape of the Lock.' It is written in the voice of the narrator, and addressed to, or overheard, as it were, by, the reader of the poem. It refers to the central incident in the poem, the seizing of Belinda`s lock of hair by Lord Petre, that constitutes the main action of the poem. Its significance is that it sets the tone of the poem as a mock epic, dealing with a contest not over great kingdoms and deeds, as in serious epic, but over trivia.

For a 300-word answer, you might expand on how the introductory couplets of the mock epic relate to the traditional invocation of the Muses of actual epic, especially with reference to Pope`s Homer.