In our very first class on Photoshop, when we are just getting familiar with Workspace, in General Preferences we come across the setting called Image Interpolation:

Interpolation has several meanings.
The word comes from inter meaning between and pole, the points or nodes. Any means of calculating a new point between two existing data points is therefore interpolation.
In the mathematical subfield of numerical analysis, interpolation is a method of constructing new data points from a discrete set of known data points.
In the context of computer graphics interpolation refers to the use of (usually) piecewise polynomial interpolation (given some data points (such as obtained by sampling), the aim is to find a polynomial which goes exactly through these points) to draw images semi-automatically.
Polynomials can be used to approximate more complicated curves, for example, vector shapes, given a few points. A related application is the evaluation of the natural logarithm and trigonometric functions: pick a few known data points, create a lookup table, and interpolate between those data points. This results in significantly faster computations.
The essential data for performing interpolations is obtained through sampling. Whereas Image Interpolation setting in General Preferences regards to polynomial interpolation used largely for completing the vector data, based on the points defined by the artist (e.g. calculation of a curve between 2 anchor points), it also refers to Image sampling necessary for scaling images, and defines the Quality of the resulting image after its size has been changed.
In computer graphics, image scaling is the process of resizing a digital image. Scaling is a non-trivial process that involves a trade-off between efficiency, smoothness and sharpness. As the size of an image is increased, so the pixels which comprise the image become increasingly visible, making the image appear “soft”. Conversely, reducing an image will tend to enhance its smoothness and apparent sharpness.
Apart from fitting a smaller display area, image size is most commonly decreased (or subsampled or downsampled) in order to produce thumbnails. Enlarging an image (upsampling or interpolating) is generally less common (it occasionally has to be done to upscale images for printing). The main reason for this is that in “zooming” an image, it is not possible to discover any more information in the image than already exists, and image quality inevitably suffers. However, there are several methods of increasing the number of pixels that an image contains, which evens out the appearance of the original pixels.
When we prepare textures for using them in Second Life or any other 3D environment, we deal with a little bit more interesting phenomenon – in most cases, particularly when it comes to clothing, we will not be looking at the image in its original size – since avatar clothing will occupy much smaller space on the computer screen than the original image (which is normally 512×512 pixels at resolution 72 pixels per inch). Yet we would like to preserve as much detail as possible, also because there is a chance that we want to zoom into the clothing texture. As we create clothing on 1024×1024 pixels documents, but then have to downscale them to 512×125 in order to upload them to SL, preserving maximum quality while changing pixel dimentions is one of our big concerns.
Image Size dialog box includes options for Image Resampling:

Resampling is the digital process of changing the sample rate or dimensions of digital imagery by analysing and sampling the original data.
A digital image is known as a bitmap (and you already know that we always deal with bitmap images in SL, besides we have seen how much Image Resampling does NOT matter for vector objects scaling), it being a literal map of which pixels are what value, to construct an image.
A bitmap is said to be sampled on each pixel, rather than being supersampled (more than one point of data per pixel) or subsampled (less than one point of data per pixel). Resampling this bitmap involves creating a sample grid, which is overlaid on the pixels. According to how far each grid point is away from the original centre of each pixel, and according to whatever resampling algorithm is in use, the new sample point is given a colour value.
The simplest method is known as nearest neighbour or point sampling. The closest pixel center to each sample grid point is used, with no input from other surrounding pixels.
As an example i used this image – a RASTERIZED text layer with gradient applied to it.
The image size is 844×124 pixels:

Since in our work for clothing we will be dealing mostly with downscaling the images, for this example, too, i scaled the image down to 20% of its original size in each case.
Nearest neighbor:

This image is shown at 500% zoom, as you can see. Nearest neighbor interpolation preserved the original image, but since the pixels were replaced by the average of the resampling you can see that the gradient lost quite a bit of its smoothness and the resulting image has considerably jagged edges.
Nearest Neighbor is a fast but less precise method that replicates the pixels in an image. This method is for use with images containing edges that are not anti-aliased, to preserve hard edges and produce a smaller file. However, this method can produce jagged effects, which become apparent when you distort or scale an image or perform multiple manipulations on a selection.
Other scaling methods are better at preserving smoothness in the image. For example, bilinear interpolation produces the following result:

*Remember, that we generally will NOT be looking at our images at such close-up.
Bilinear method adds pixels by averaging the color values of surrounding pixels. It produces medium-quality results.
Linear (or bilinear, in two dimensions) interpolation is typically better than the nearest-neighbor system for changing the size of an image, but causes some undesirable softening of details and can still be somewhat jagged. Better scaling methods include bicubic interpolation.
The bicubic algorithm is frequently used for scaling images and video for display. It preserves fine detail better than the predominant bilinear algorithm.
Bicubic is a slower but more precise method based on an examination of the values of surrounding pixels. Using more complex calculations, Bicubic produces smoother tonal gradations than Nearest Neighbor or Bilinear.
In Photoshop we have finer choices for bicubic interpolation:
Bicubic Smoother – a good method for enlarging images based on Bicubic interpolation but designed to produce smoother results. This methos is required in Photoshop not as much for digital images per se (even though sometimes that can also be necessary), but mostly because this program is widely used for printing, where one more often has a situation when the original image has to be enlarged.
In making clothes for Second Life we have to deal with DOWNSCALING our original work, which is normally done in the documents 1024×1024 pixels, and has to be reduced to 512×512 pixels with minimum detail loss. In this case our choice should be Bicubic Sharper – a good method for reducing the size of an image based on Bicubic interpolation with enhanced sharpening. This method maintains the detail in a resampled image:

In this snapshot from Second Life you can see fine detail of the metal buckles and texture of the pants reasonably well, due to the fact that the original clothing textures were resized using bicubic sharper interpolation.
CONCLUSION
1. For best Image quality for SL clothing textures (but not in every other case for textures – that will depend on the screen space occupied by your texture under average zoom) it is better to set Image Interpolation in General Preferences to Bicubic Sharper. This is a SLOWER algorithm, but it produces higher quality images.
2. For downscaling your ready work you can use a few methods:
1) After merging all the layers of the ready image – group it into vector smart object before resizing and you don’t have to bother about any interpolation whatsoever.
2) If you are still dealing with bitmap data, set Image Resampling in Image Size dialog box to Bicubic Sharper.
3) If you are saving your 1024×1024 document DIRECTLY in .png format, before you resized it, via Save for Web, use Image Size tab for changing the size and set quality to Bicubic Sharper:

Note: If you have Image Interpolation set to Bicubic Sharper in General Preferences both Image Size and Save for Web dialog boxes will show this choice by default.