The technical term for this is “resampling.” Resampling is an advanced mathematical equation (algorithm), applied when you’re upsampling (increasing) or downsampling (decreasing) the size of your images. The algorithm analyzes all of the pixels in your image and either adds or subtracts pixels to match your desired resolution, based on the color and luminance values of the surrounding pixels.
In Photoshop, there are five different resampling methods: Nearest Neighbor; Bilinear; Bicubic; Bicubic Smoother; and Bicubic Sharper. Understanding what each of these five options does will help you make a more informed decision about which to choose for your purposes.
Nearest Neighbor and Bilinear are older forms of resampling technology. These were early features of Photoshop and are useful for graphics, not photos (the first versions of Photoshop were for graphic designers—not photographers—as digital photography didn’t really exist when Photoshop was introduced). Adobe rarely takes out any features in Photoshop because users still may be using them in some capacity, so they remain in the options.
According to Adobe, the best option today for resampling is Bicubic and its three different versions, including one for enlarging (Bicubic Smoother) or decreasing (Bicubic Sharper) the amount of pixels in your image, and Bicubic for enlarging photos.
An example of when it would be best to use Bicubic is when you don’t want to disturb a lot of different tonal ranges, for example, in a photo with a large amount of sky; if you were to use Sharper or Smoother, these tonal ranges would be affected, while Bicubic would preserve clean gradient transitions.
Here are some quick tips to resizing in Photoshop: Bicubic is best for smooth gradients; Bicubic Smoother for enlargements; Bicubic Sharper for reduction; and Nearest Neighbor is the best way to preserve hard edges.
Beyond Photoshop, there are a number of very good plug-ins like onOne Software’s Genuine Fractals and Alien Skin’s Blow Up, which are adept at resizing images. If you do a lot of resampling, especially to increase image size, consider investing in one of these specialty plug-ins.