The difference between a dye and a pigment is that dye dissolves in a liquid and pigment doesn’t. Therefore, dye doesn’t settle in a can or jar, but pigment does and has to be stirred back into suspension before using.
Dyes are available in powder and liquid form. If in powder form, you have to dissolve the dye in the appropriate liquid—usually water, alcohol or acetone. Instructions will tell you which. In liquid form, dyes are available concentrated (for you to thin), and already thinned with the appropriate liquid.
What makes dyes and pigments confusing is that they can be used together in a stain, and they often are in common off-the-shelf stains available in paint stores and home centers.
This doesn’t cause any problem for application, and it doesn’t make much difference for appearance. But you need to be aware that the dye part of a stain can bleach out in sunlight, leaving only the pigment part remaining. This will almost always change the appearance of the stain on the wood quite noticeably.