The hydropathy index of an amino acid is a number representing the hydrophobic or hydrophilic properties of its sidechain. It was proposed in 1982 by Jack Kyte and Russell F. Doolittle.[1]
The larger the number is, the more hydrophobic the amino acid. The most hydrophobic amino acids are isoleucine (4.5) and valine (4.2). The most hydrophilic ones are arginine (-4.5) and lysine (-3.9). This is very important in protein structure; hydrophobic amino acids tend to be internal (with regard to the protein's 3 dimensional shape) while hydrophilic amino acids are more commonly found towards the protein surface.
References
1. Kyte J, Doolittle RF (May 1983). "A simple method for displaying the hydropathic character of a protein". J. Mol. Biol. 157 (1): 105–32. PMID 7108955.