The "bundle of perceptions" theory is one of David Hume's most significant contributions. Hume was an empiricist, meaning that he saw human perception as the source of human understanding. This idea, perhaps most famously expressed by John Locke as a "tabula rasa," rejected the notion that humans were born with innate understandings of the world around them. Thus everything, including what we imagine as human nature and the mind, was the result of perception:
...they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement.
By "they," Hume meant concepts or ideas, held by some to be innate. In this passage, he was specifically rejecting the French philosopher Rene Descartes, who had argued for the existence of these concepts, which he held to be essentially divine in origin. Hume thought that human understanding, and thus human nature, was the effect of interactions with the world around us. The mind did the work of associating different perceptions with each other, and much of the work this quote is from, A Treatise of Human Nature, was devoted to working out a theory of how this process took place. As the title of the book suggests, this was not merely a treatise on human understanding. Hume's "bundle theory" had profound implications for thinking about human nature. If all understanding was derived from perception, and people absorbed these perceptions with an "inconceivable rapidity," then not just human understanding, but human nature itself, was in "perpetual flux and movement."
Hume is very interesting, because Hume's philosophy, taken as a whole, tends to take empiricism towards its logical extremes—to the point that it begins to collapse into a kind of philosophical skepticism. We can see this in his decoupling of cause from effect, and we can see this in his "bundle theory" (with deals with the treatment of the self).
Ultimately, for Hume (like other empiricists), knowledge is entirely shaped by sensory experience. It is through our senses that we experience the world. From these foundations, Hume's philosophy brought him to reject altogether the notion of an internalized self. For Hume, the self is an illusion.
Instead, Hume suggests that individual consciousness amounts to nothing more than the aggregate of one's perceptions and impressions, and if one were to stop and reflect upon one's own internal conscious existence, all that person would be able to discern would be those nets of perceptions and impressions and the associations linked between them.
This saying is a reference to bundle theory, a philosophy largely attributed to Hume. Bundle theory asserts that anything tangible is comprised of its properties and nothing more. For example, imagine a tennis ball. It is impossible to think about the ball without considering its specific properties, such as weight, color, texture, and material. This means that the object is a culmination, or "bundle," of perceptions that we have made about it and nothing more.
According to bundle theory, these bundles are no different with regards to human beings. The idea of an enduring self is a complete illusion, according to bundle theory, because a human being is no more than the perceptions that make it up. The mental states we experience are bundled into a loose concept of self. Accordingly, objective existence is impossible to perceive.
David Hume's Bundle Theory is a theory of human nature, or more specifically, of the relationship between perception and the unique "self" that humans believe they possess. Most people consider the mind to be a uniquely perceptual construct, entirely separated from any other person or thing. The mind would therefore exist outside of the physical realm and instead is subject to theories of metaphysics. Hume argued that all human nature, including the theory of self-identity, is the result of a collection of perceptions created by the senses; the mind is its perceptions, and without the perceptions the mind would not exist.
...I may venture to affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a perpetual flux and movement. Our eyes cannot turn in their sockets without varying our perceptions.
When I turn my reflection on myself, I never can perceive this self without some one or more perceptions; nor can I ever perceive any thing but the perceptions.
(Hume, "Of Personal Identity," anselm.edu)
In other words, the constant flow of perception (sensory stimulus) creates the reactive processes that are termed the mind. The human self -- action, reaction, "original" thought -- is constantly created and recreated due to its properties of perception; those properties are necessary to allow the "mind" or "human nature" the status of objecthood. Hume goes on to state that each person exists in a purely subjective world; his perception of himself is entirely based in the grouping of perceptions that make up himself, and he cannot perceive another person without perceiving the perceptions that make up that person's self-identity. The essential theory is that each person exists in an isolated bubble of perceptions, and does not necessarily perceive the outside world as it objectively exists. Instead, the mind's perception of itself colors the world to make sense inside its own perceptions.