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Definitions of bilinear filtering:

An averaging technique applied to the color values of adjacent pixels so that textures look smooth rather than blocky. It aims to make the texture looks more realistic
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technique that smoothens close-zoomed bitmaps.
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Bilinear filtering is a method of anti-aliasing texture maps. A texture-aliening artifact occurs due to sampling on a finite pixel grid. Point-sampled telexes jump from one pixel to another at random times. This aliening is very noticeable on slowly rotating or moving polygons. The texture image jumps and shears along pixel boundaries. To eliminate this problem, bilinear filtering takes a weighted average of four adjacent texture pixels to create a single telex.
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technique which allows to solve the problem of the smallest texture in a polygon where they have to be applied. In this case you would have seen a "blocks" effect due to the texture expansion on the surface; thanks to an interpolation operation between a texel and the 4 next to it, the bilinear filtering shows the correct texel.
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Bilinear filtering is a texture mapping method used to smooth textures when displayed larger or smaller than they actually are.
en.wikipedia.org/wiki/Bilinear_filtering