Pablo Picasso and other artists experimenting with Cubism were interested in deconstructing three-dimensional space and changing viewers' perceptions of the world, space, and time.

Answer 1

One way to look at the history of Western painting is as a series of answers to the question, "Should visual art try to represent our spatial 3-dimensional reality as we experience it in a 2-dimensional format (paintings, drawings) -- or should we be doing something else?" {This discussion is, of course, a great simplification of the subject. MLR}

The Middle Ages mostly says "No, the reality that counts is a spiritual reality and everything in the painting should reflect and promote that." See anything by Cimabue for excellent examples of this.

The Renaissance maintains a religious focus, but gets very interested in the world it inhabits, and devises ways to reproduce that on panel and canvas. This means, among other things, oil paints and linear perspective (and other means of perspective, but linear's the biggie). Take a look at works by Masaccio, Raphael's The School of Athens, or da Vinci's The Last Supper for superlative examples of this being worked out and perfected.

The next 400 years mostly says, "Yes, we want build on linear perspective and recreate the experience of 3D space on 2D surfaces." It's not until the Impressionists of the late 1800s that Western Art starts to reconsider the question of spatial realism and what else you might do on a canvas.

The Impressionists had many different goals and interests, but you could summarize them very generally as a fascination with how the eye actually sees what it sees. Theirs was the era of the development of photography and film, after all. Some focused on how the eye sees light, others among the Post-Impressionists, particularly, become fascinated with how color and the eye work together. The movement takes its name from Claude Monet's 1872 painting, Impression, Sunrise, in which he is definitively focused on the play of light, air, and water. His answer to the question is still "Yes, let's paint the world we see as we see it", but the emphasis is firmly on the experience and mechanism of seeing, and not the recognition or symbolism of the objects or scene.

The Post-Impressionists aren't really a coherent group because they take the experiments of the Impressionists and run with them in 80 different directions. The through-line to Cubism is Paul Cezanne. Cezanne (see L'Estaque, 1883-1885) is still interested in painting the reality of the world, but he's breaking down its forms into geometric shapes given mass by chunks of color (Cubism paid a lot of attention to this). He's also equally interested in the surface of the painting itself as an object of fascination, not just the subject represented in the painting: line, color, brushstrokes, the paint itself. So Cezanne answers the question about spatial realism with a "Why not both realism AND something else?", and in doing so, he blurs the difference in meaningful and influential ways.

The Expressionists of the late 1800s-early 1900s take all this experimentation and say, "Well, sure, the world we live in, of course...but what's really important is what the art image triggers inside us." They're focused on how they feel or experience their world; represention of realistic objects in realistic space takes a back seat to emotion and spirituality. The Expressionists really decouple form, line, color, and spatial representation from external meaning. See Wassily Kandinsky, who explores spirituality via abstracted or nonrepresentational forms, using music as his template, for one strand (try Yellow-Red-Blue (1925)). See how Henri Matisse prioritizes color and form over realism, in order to create calm and joy, for another strand. (Try Open Window, Collioure (1905) for an illustrative example.)

FINALLY! We reach the Cubists. It's the early 20th century. Cars are beginning to happen -- it's the Machine Age. World War I is just around the corner. Albert Einstein publishes his Special Theory of Relativity in 1905 -- e = mc² -- which, simplifying greatly, says that space and time are malleable, depending on the relative positions of particular objects in space and time.

During the same period (1907), the French philosopher Henri Bergson posits consciousness as an accumulation of experiences/ perceptions. That is, we assemble our understanding of the world and the things in it over time. Ask yourself how you know a house is a house. If you just walk up to the front door, all you can perceive is that there's a vertical wall with a door. You don't actually perceive the left wall, the right wall, the back wall, or the roof -- you remember that things called houses have these other pieces. How can you trust that this is the same situation? Because you've encountered it many, many times before, and nothing called a house was only a wall with a door. Your perception of the wholeness of the object is assembled from accumulated memories, not immediate perception.

With these two ideas in mind (space & time are malleable, consciousness is an accumulation of experienced perceptions), Pablo Picasso, Georges Braque, and other Cubists look back at the recent history of art, and answer that question. They say, "Unlike the Expressionists, we're still interested in realism, but what's real is how we assemble our perceptions into truth in an environment of malleable space & time, not some external verity, so how can we paint that?". So I'd nudge the poster's question a tiny bit and say that the Cubists weren't so much trying to change people's perceptions of time and space, but rather were trying to accurately represent how we perceive objects in time and space. As Picasso said, "I paint objects as I think them, not how I see them." See Picasso, Les Demoiselles d'Avignon (1907) for a proto-Cubist piece ; Braque, Houses at L'Estaque (1908) identified as having "little cubes" & arguably the first Cubist work; and Picasso, The Accordionist (1911) for pushing the realistic component of Cubism almost completely off the canvas.