There are a number of ways to interpret this question, as King Lear is a more thematically complex play than, say, Othello or Macbeth. However, I would say the main conflict is between Lear's false vision of reality and physical reality itself. Many themes then spin out of that main conflict between illusion and reality, a conflict that is laid out for us in the first act.
In this act, Lear is ready to retire from active monarchial duty and turn his kingdom over to his three daughters, as long as they pledge love and fealty to him. The first two do this readily, with flattering but empty words; the third refuses to flatter. Lear, too long removed from reality, believes his two duplicitous eldest daughters' words and rejects Cordelia in fury. His Fool tells Lear that he is the biggest fool of all in dividing his kingdom and giving up his power—and in exiling Cordelia.
The Fool proves to be wiser than the king, who has to find out the hard way that his power does not reside in people's innate love of his person, but in the actual manifestations of his power—land, wealth, and armies—that he has given away. Lear's daughters' dizzying speed in casting him aside, even cruelly throwing him out to fend for himself on the heath in a storm, reeducates Lear in what reality is.
Lear learns to regret trusting his eldest daughters and rejecting the loyal one, and as he suffers on the heath, without food or shelter, he learns to regret that he did not do more for the poor of his kingdom while he had the chance.
Lear ends up a far wiser and sobered man after he is stripped of his power, but even at the end of the play, it is difficult for him to accept reality: although Cordelia is obviously dead, he still wants to test this fact by putting a mirror to her mouth to see if it will pick up the mist of breath.
Through Lear's conflict with concrete, physical reality, audiences are reminded to trust in deeds and materiality rather than words and flattery.