Palettes are simply a set of 256 colors which can be used in the picture. You don't have to use all 256 as unique colors. If you so choose, you could only use two separate colors, and the other 254 would just be duplicates.

JJ2 uses the colors from the palette when rendering the sprites. Normally, the first two colors in the palette will be transparent. The next 14 are not used. Then there are 8 different shades of green, 8 shades of red, 8 of blue, etc, etc, up to the 96th color. However, if you were to replace the 8 which are normally green with yellow, Jazz would appear yellow, not green. Therefore, you should usually use the standard Jazz palette for the first 96 colors, else levels made your tileset will have really ugly sprites. The later colors can be made into whatever you want. There's room for textured backgrounds and such, although you can worry about those later.

If you just want to prevent this ugliness in sprites, I suggest TilesetPal. This is designed specifically with JJ2 tilesets in mind, and is the fastest, easiest way to give the palette the correct number of colors and to get sprites to look good. It also comes with the standard Jazz Palette, which is very useful.

If you want to do some more complex stuff with palettes, PalSuite is a great program. It will allow you to edit palettes and apply them to the image file you will build your tileset from.