Pigment ink is higher premium type of dye based ink. 

Dye based inks are able to provide a wider colour space for more vibrant and colourful prints. 

Most inkjet printers use dye based ink, but professional users like photographers prefer pigment based ink. Dye ink key advantages is wider color range and lower cost. Meanwhile the dye ink is water resistance like pigment ink. 

Advantage of pigment ink:

Long lasting print and better color stability

Resistant to fade when expose to the UV light (sunlight)