The pKa of the side chain is relatively close to 7.4—it's about 6—so, at physiologic pH, one nitrogen atom is protonated and the other isn't. Under more acidic conditions, the second nitrogen atom can become protonated, giving the side chain a positive charge.
Classifying amino acid side chains as hydrophobic or hydrophilic is actually a very complex matter. The amino acids with long alkyl side chains—alanine, isoleucine, leucine, valine, and phenylalanine—are all strongly hydrophobic and thus more likely to be found in the interior of proteins, away from water on the surface of the protein. The amino acids with charged side chains—positively charged histidine, arginine, and lysine, plus negatively charged glutamate and aspartate—are hydrophilic, as are the amides asparagine and glutamine. The remaining amino acids lie somewhere in the middle and are neither particularly hydrophilic nor particularly hydrophobic.
Primarily used when space is at a premium as with formulas of long protein sequences, the labeling of individual amino acids in figures, and mutation shorthand