Oberon and Titania are a married couple, the king and the queen of all the fairies. At the beginning of Act II, the two are in an argument, which causes all of Nature to be disrupted. The royal couple have such dominion over the whims of nature that their discord causes the world to be in turmoil while they are not reconciled. It is this domestic argument which provides the impetus for much of the action of the play.
Oberon and Titania are at such odds that when they meet Oberon says to her "Ill met by moonlight" (II.i.62) Titania acuses Oberon of having a mistress, and he calls her proud. All this rancor has caused serious havoc within the natural world:
As in revenge, have suck'd up from the sea(90)
Contagious fogs; which, falling in the land,
Hath every pelting river made so proud
That they have overborne their continents.
The ox hath therefore stretch'd his yoke in vain,
The ploughman lost his sweat, and the green corn(95)
Hath rotted ere his youth attain'd a beard;
The fold stands empty in the drowned field,
And crows are fatted with the murrion flock;
The nine men's morrisis fill'd up with mud,
And the quaint mazes in the wanton green,(100)
For lack of tread, are undistinguishable.
The human mortals want their winter here;
No night is now with hymn or carol blest;
Therefore the moon, the governess of floods,
Pale in her anger, washes all the air,(105)
That rheumatic diseases do abound.
And thorough this distemperature we see
The seasons alter: hoary-headed frosts
Fall in the fresh lap of the crimson rose;
And on old Hiems' thin and icy crown(110)
An odorous chaplet of sweet summer buds
Is, as in mockery, set. The spring, the summer,
The childing autumn, angry winter, change
Their wonted liveries; and the mazed world,
By their increase, now knows not which is which.(115)
And this same progeny of evils comes
From our debate, from our dissension;
We are their parents and original.
(Act II Scene i)
The source of this argument is a boy, whom Oberon wants to have as his attendant. The boy is the son of a priestess of Titania. The priestess died in childbirth, and Titania has brought the child up in memory of her dead friend. Titania, for love of the dead priestess and the boy, will not give the child up to Oberon.
This fairy argument is meant to show the caprices of nature, and how the disruption of nature (and Shakespeare, of course, uses the argument of the fairy royalty as a metaphor) can cause incredible suffering to mankind. This cosmic disturbance must be resolved by the end of the play; the introduction of it so early in the play shows us that this argument will have bearing on everything that happens to the characters in the play.