Of the Enlightenment philosophers Locke, Berkeley, Hume, and Kant, which was the most influential with respect to description of the nature of reality?
Hume, in combination with Kant—who was strongly influenced by him—changed the whole nature of how reality is perceived. Hume's unrelenting skepticism effectively destroyed the pretensions of metaphysics to arrive at any reliable picture of reality. As traditionally conceived, metaphysics, according to Hume, was unable to do this because it was grounded in supernatural assumptions and as such could tell us nothing about the empirical world around us, which for Hume is the only source of reliable knowledge. For Hume, the arch-empiricist, knowledge comes from sense experience and the faint impressions they leave in the mind. In his thought, there is no place for a priori metaphysical postulates as they are purely products of the mind, not related in any way to empirical experience.
As we've already seen, Kant was very much influenced by Hume. He understood that Hume's skepticism radically altered the very nature of Western philosophy. To a large extent, Kant's entire philosophical system is a response to Hume. Kant does not want to get rid of metaphysics altogether, but he does recognize the need to restrict its explanatory power. To this end, he restricts it to the realm of what he calls synthetic a priori propositions, that is to say propositions which can tell us something about the world around us, the empirical world, but whose truth can be verified independently of experience.
In other words, what Kant is doing is putting forward a happy medium between the old, dogmatic metaphysics, which argued that it was possible to arrive at a true picture of reality purely by the exercise of reason without empirical experience, and Hume's radically skeptical picture, which denies the possibility of any kind of a priori knowledge.
In certain ways, the work of Immanuel Kant can be considered a synthesis of the best that is found in the other three. The major problem with Berkeley is that his idealism requires, to make any form of knowledge meaningful, the possibility that we can know things in themselves, as opposed to mere perceptions. Hume's notion of reality has influenced many modern philosophers, especially his arguments that such regularities as causation are things we impose on our perceptions. Although Kant's "dogmas" (the synthetic-analytic and a priori-a posteriori distinction) have been criticized by Quine, inter alia, nonetheless, most philosophers argue that his notion of the synthetic a priori, and the way it accounts for how we participate in the construction of reality, has been the foundation of most subsequent philosophical systems.