I assume you are asking this question because you don't understand what a palette is in computer graphics terms?
A palette is an array of colour values, normally of with as much dynamic range as possible (i.e. 8bits per colour, or more). A palette is used in textures as a form of texture compression. Instead of having a high/true colour image of the texture, the actual colour values are replaced with index values in to a palette of colours (where the colours are chosen to best represent the colours in the image ... this is a subject all in itself!).
Why do this? Well, a 256x256 texture would consume 128Kb of memory to store in high colour 16bit. If it were converted to a 8bit paletted texture (256 colours), it would only consume half that amount of memory, 64Kb. Reduce it to a 4bit paletted texture (16 colours), and it drops by half again, 32Kb.
Paletted textures also make certain effects dead easy, such as colour cycling: rather than having to generate a complete new texture, you just modify the palette data and the whole image changes. Also, generating another texture of the same image, but a different hue, is easy, just by selecting another palette for the same texture.
The PSX supports all 3 of those types of textures I mentioned above: 16bit direct, 8bit paletted, and 4bit paletted. Since VRAM is fairly limited (1Mb), it needs to to allow the game developers to be "creative"
Not all PC 3d accelerators support paletted textures at all, or if they do their support is buggy, or they only support 8bit. In fact, I only know of Matrox supporting 4bit paletted textures, but there may be more.
Therefore, Pete's plugins have the option for using the paletted capabilities of your graphics card, if available and bug-free. Sometimes it will be quicker, sometimes slower, since downloading palettes to the graphics card can be an overhead.
My plugin always uses paletted textures, for the PSX's paletted textures.