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At any time, a game will likely have many objects rendering textures.
So what is a texture? an image for example?

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Yes, a texture for most purposes is an image.

Once a texture is loaded from a file, it can be applied as a sort of "decal" to any polygon you wish.

When you see textures in an image file they typically appear a bit warped,

a texture

That's because when the texture is "wrapped" around the model, it will all even out and wrap around the model properly. You use a technique called UV mapping to be able to create a nice texture that will wrap around the model properly.

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    \$\begingroup\$ In the world of programmable shaders, a texture is a 1D/2D/3D grid of pixel values. These textures can be sampled with different interpolation filters (nearest, bilinear, trilinear, anisotropic) to retrieve values from the texture. Common use-cases are as normal albedo (color) images, gradient maps and palettes, normal maps for bump-mapping, and much much more. \$\endgroup\$ – Lars Viklund Aug 8 '11 at 8:56
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    \$\begingroup\$ Yes, but given the context of the question, I think he meant "texture as a picture" \$\endgroup\$ – bobobobo Aug 8 '11 at 15:37
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Yes, it typically is an image (often of a pattern) applied to the surface of a 2D or 3D model.

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Textures are basically images that are used in 3D games on 3D objects, 2D planes in 3D space, or GUI elements.

Textures can also be generated at real time.

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