agitated from the heat when this happens:

And then the Arab drew his knife and held it up toward me, athwart the sunlight.

A shaft of light shot upward from the steel, and I felt as if a long, thin blade transfixed my forehead. At the same moment all the sweat that had accumulated in my eyebrows splashed down on my eyelids, covering them with a warm film of moisture. Beneath a veil of brine and tears my eyes were blinded; I was conscious only of the cymbals of the sun clashing on my skull, and, less distinctly, of the keen blade of light flashing up from the knife, scarring my eyelashes, and gouging into my eyeballs.

He ends up shooting the Arab man several times for apparently no reason other than that the sun's heat and light makes him so uncomfortable that he becomes violent. It could be argued that the sun is then additionally a symbol of Meursault's final realization that life is absurd: people do things without reason or rationality, and life has no inherent meaning beyond the present moment.

When evaluating the significance of the sun in Camus' The Stranger, we might focus on the connection between the day of the funeral (when Mersault's mother is buried) and the day that Mersault commits the murder. 

On each of these days the sun is mentioned as being very hot, oppressive, and even painful. 

We might conjecture that when Mersault encounters the extreme heat/sun on the beach he is (consciously or unconsciously) reminded of his mother's death and burial. The latter sections of the novel offer ample suggestion that Mersault is affected by his experiences (like his mother's death and his affection for Marie) even though he denies that these experiences are influencing him.

The espoused emotional and intellectual neutrality of Mersault's narration of his own psyche is brought into question by contrasting examples of deeply felt emotion and keenly observed, very human turmoil.

The second part of the novel deals with Mersault's denial of an inner life and the ramifications of this denial are indirectly examined in this section. However indirect the treatment of this idea may be, the notion that Mersault's actions are connected to an emotional inner-life is repeatedly suggested by almost all the characters that Mersault encounters in Part 2. Thus, while Mersault maintains an inner-dialogue that consistently denies emotional causes for his behavior, the novel creates a significant sense of doubt as to Mersault's ability to understand himself. 

His behavior may be, ultimately, outside of his own control. His impulses may be inspired by emotional connections (such as the sun-mother's-death connection) that he either does not see, does not understand, or is unwilling to consider. The justice system's attempts to apply a strict morality to a person like this (who does not recognize his own emotional/psychological state of being) begins to illuminate Camus' notion of the absurd at work in The Stranger. 

In any event, the sun is powerfully present when Mersault's mother is buried as well as on the day of the murder. The meaning of this connection and this symbolism is, perhaps, open to interpretation. The coincidence cited here may be intended to be understood as just that - a meaningless coincidence.

Remember, The Stranger is a novella told in flashback.  Meursault narrates it, as if from death row, where he no longer sees the sun at all, and this colors Meursault's use of symbolism.  Whereas the sun should be a source of life, it becomes a symbol connected with death in hind sight.

In The Stranger, the sun is present whenever Meursault faces difficult decisions.  It is an external force that pressures the narrator and others to, ultimately, make bad decisions.  In a way, the sun represents the external forces that are placed on the individual during the moral decision-making process: religion, culture, social expectations, tradition, the justice system.  One cannot make decisions in a vacuum; all these pressures weigh on him constantly, and Camus' use of the sun is a kind of amalgam of all these pressures.

In Camus' absurd universe, most people are faced with two paths: the one leading toward individual freedom (life) and the one leading toward mass conformity (death).  The sun, in retrospect, is an oppressive representation of all the forces which limit one's individual freedom and ability to choose life over death.

For example, Merusault (and Perez) must walk in the oppressive heat during the funeral procession.  No one would, under any other circumstances, dress in black and follow a dead body in the heat of day by choice; it is a cultural expectation.  Perez even passes out from the walk of death.  The sun is a way of underscoring the absurdity of the rituals of death.  (Remember, in the end, Meursault will say that no one had the right to cry over his mother's death.)

The sun is also present on the beach with the Arab.  Here, the sun light off the blade of the knife is a stabbing reminder of the external forces placed on the individual: Meursault feels compelled to shoot out of self-defense, or revenge, or hatred of Arabs.  It's as if all the forces of society are aligned against the individual in this showdown, and one's choice to not shoot or shoot once or five times is the choice between life and death.

Contrast this with Meursault's freedom in the next chapter where he goes to the beach and swims with Marie.  The sun (and water) is a symbol of life and freedom, and Meursault relishes it against his body.  In the "Myth of Sisyphus," a similar story, Sisyphus puts death in chains so that he can see his wife, the curve of the earth, the sun, and the water again.  He chose freedom over death, and the sun stands in sharp contrast to the shades of Hades.