Skim through

What it does: chelating, viscosity controlling 

Also called: disodium EDTA

The science

EDTA disodium is a salt of EDTA (ethylenediamine tetraacetic acid). It is a chelating ingredient that attracts the minerals away from the hair shaft and helps them rinse away

Disodium EDTA and the related ingredients bind to metal ions which inactivates them. The binding of metal ions helps prevent the deterioration of cosmetics and personal care products. It also helps to maintain clarity, protect fragrance compounds, and prevent rancidity.

In cosmetics and personal care products, these ingredients are widely used and can be found in moisturizers, skin care and cleansing products, personal cleanliness products, bath soaps, shampoos and conditioners, hair dyes, hair bleaches, and many other product types.

TLDR

Disodium EDTA is a helper ingredient that helps products to remain nice and stable for a longer time. It does so by neutralizing the metal ions in the formula (that usually get into there from water) that would otherwise cause some not so nice changes. It is also used as a preservative and as a pH adjuster.  It is typically used in tiny amounts, around 0.1% or even less.