What is a dye based ink?
Inks are largely divided into two categories: dye-based and pigment-based.
Additionally, there is invisible ink, which usually consists of a variety of other ingredients that need to undergo a chemical reaction in order to become visible.
Dye is a soluble colourant, which means a dye-based ink is a solution, whereas pigments are colourants that consist of small particles, making pigment-based inks chemical suspensions (see also here).
Why the difference is important, is because both have different characteristics.
Without going into the chemical differences too much, the benefits of dye-based inks include:


Beautiful color quality
Easy to spread and paint with
Affordable and easy to find
Adheres to almost any surface


And the disadvantages are:


A tendency to fade out fast
A lack of resistance to external factors
More prone to bleeding


For pigment-based inks, the benefits are:


Resistant to most exterior factors
Can last for decades in paper
Doesn't fade out over time
Dry and adhere fast to surfaces


And the disadvantages:


Color can be a bit dull
Pretty expensive &amp; difficult to find


Lists mostly copied verbatim from here