EDTA (ethylenediaminetetraacetic acid) is a chelating agent, which is a substance whose molecules can form several bonds to a single metal ion. It's formed of four carboxylic acid groups attached to two nitrogen atoms. In certain conditions the compound develops negative charges on four of the oxygen atoms; this allows EDTA to sequester (grab onto) free metal ions or minerals. Think of it as a lobster with claws closing around minerals as they float past in the water.
Widely used in bath and beauty products, EDTA prevents changes in color, texture and fragrance. Removing free metal ions or minerals has several benefits: it helps products stay bright and beautiful, it reduces hardness of water, giving skin a better feel and it helps reduce scum that some soaps naturally develop when used in the bath.