The primary/secondary quality distinction is a conceptual distinction in epistemology and metaphysics, concerning the nature of reality. It is most explicitly articulated by John Locke in his Essay concerning Human Understanding, but earlier thinkers such as Galileo and Descartes made similar distinctions.

Primary qualities are thought to be properties of objects that are independent of any observer, such as solidity, extension, motion, number and figure. These characteristics convey facts. They exist in the thing itself, can be determined with certainty, and do not rely on subjective judgments. For example, if a ball is round, no one can reasonably argue that it is a triangle.

Secondary qualities are thought to be properties that produce sensations in observers, such as color, taste, smell, and sound. They can be described as the effect things have on certain people. Knowledge that comes from secondary qualities does not provide objective facts about things.

Primary qualities are measurable aspects of physical reality. Secondary qualities are subjective.

• "By convention there are sweet and bitter, hot and cold, by convention there is color; but in truth there are atoms and the void" —Democritus, Fragment 9.^[1]

• "I think that tastes, odors, colors, and so on are no more than mere names so far as the object in which we locate them are concerned, and that they reside in consciousness. Hence if the living creature were removed, all these qualities would be wiped away and annihilated" —Galileo Galilei, The Assayer (published 1623).^[2]
• "[I]t must certainly be concluded regarding those things which, in external objects, we call by the names of light, color, odor, taste, sound, heat, cold, and of other tactile qualities, [...]; that we are not aware of their being anything other than various arrangements of the size, figure, and motions of the parts of these objects which make it possible for our nerves to move in various ways, and to excite in our soul all the various feelings which they produce there." —René Descartes, Principles of Philosophy (published 1644/1647).^[3]
• "For the rays, to speak properly, are not coloured. In them there is nothing else than a certain power and disposition to stir up a sensation of this or that colour." —Isaac Newton, Optics (3rd ed. 1721, original in 1704).^[4]
• "[i]t is even possible to demonstrate that the ideas of size, figure and motion are not so distinctive as is imagined, and that they stand for something imaginary relative to our perceptions as do, although to a greater extent, the ideas of color, heat, and the other similar qualities in regard to which we may doubt whether they are actually to be found in the nature of the things outside of us."^[5] ----Leibnitz, Discourse on Metaphysics, 1686
• “It is universally allowed by modern enquirers, that all the sensible qualities of objects, such as hard, soft, hot, cold, white, black, &c.are merely secondary, and exist not in the objects themselves, but are perceptions of the mind, without any external archetype or model, which they represent.” Hume (EHU 12.15)

George Berkeley was a famous critic of the distinction. Berkeley maintained that the ideas created by sensations are all that people can know for sure. As a result, what is perceived as real consists only of ideas in the mind. The crux of Berkeley's argument is that once an object is stripped of all its secondary qualities, it becomes very problematic to assign any acceptable meaning to the idea that there is some object. Not that one cannot picture to themself (in their mind) that some object could exist apart from any perceiver—One clearly can do this—but rather, that one cannot give any content to this idea. 

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Kant, in his Prolegomena to Any Future Metaphysics That Will Be Able to Present Itself as a Science, claimed that primary, as well as secondary, qualities are subjective. They are both mere appearances that are located in the brain of a knowing observer. In § 13, Remark II, he wrote: "Long before Locke's time, but assuredly since him, it has been generally assumed and granted without detriment to the actual existence of external things, that many of their predicates may be said to belong not to the things in themselves, but to their appearances, and to have no proper existence outside our representation. Heat, color, and taste, for instance, are of this kind. Now, if I go farther, and for weighty reasons rank as mere appearances the remaining qualities of bodies also, which are called primary, such as extension, place, and in general space, with all that which belongs to it (impenetrability or materiality, space, etc.)—no one in the least can adduce the reason of its being inadmissible."

Kant argues that the understanding must provide the concepts, which are rules for identifying what is common or universal in different representations.(A 106) He says, “without sensibility no object would be given to us; and without understanding no object would be thought. Thoughts without content are empty; intuitions without concepts are blind.” (B 75) Locke’s mistake was believing that our sensible apprehensions of objects are thinkable and reveal the properties of the objects themselves. In the Analytic of Concepts section of the Critique, Kant argues that in order to think about the input from sensibility, sensations must conform to the conceptual structure that the mind has available to it. By applying concepts, the understanding takes the particulars that are given in sensation and identifies what is common and general about them. A concept of “shelter” for instance, allows me to identify what is common in particular representations of a house, a tent, and a cave.

The empiricist might object at this point by insisting that such concepts do arise from experience, raising questions about Kant’s claim that the mind brings an a priori conceptual structure to the world. Indeed, concepts like “shelter” do arise partly from experience. But Kant raises a more fundamental issue. An empirical derivation is not sufficient to explain all of our concepts. As we have seen, Hume argued, and Kant accepts, that we cannot empirically derive our concepts of causation, substance, self, identity, and so forth. What Hume had failed to see, Kant argues, is that even the possibility of making judgments about objects, to which Hume would assent, presupposes the possession of these fundamental concepts. Hume had argued for a sort of associationism to explain how we arrive at causal beliefs. My idea of a moving cue ball, becomes associated with my idea of the eight ball that is struck and falls into the pocket. Under the right circumstances, repeated impressions of the second following the first produces a belief in me that the first causes the second.

The problem that Kant points out is that a Humean association of ideas already presupposes that we can conceive of identical, persistent objects that have regular, predictable, causal behavior. And being able to conceive of objects in this rich sense presupposes that the mind makes several a priori contributions. I must be able to separate the objects from each other in my sensations, and from my sensations of myself. I must be able to attribute properties to the objects. I must be able to conceive of an external world with its own course of events that is separate from the stream of perceptions in my consciousness. These components of experience cannot be found in experience because they constitute it. The mind’s a priori conceptual contribution to experience can be enumerated by a special set of concepts that make all other empirical concepts and judgments possible. These concepts cannot be experienced directly; they are only manifest as the form which particular judgments of objects take. (http://www.iep.utm.edu/kantmeta/)