Why do neumes have colored lines?

In the 11th century, neumes were "heighted" to suggest specific melodic lines. A musical staff of four lines evolved about the year 13th century. Neumes placed on the staff showed exact pitch, allowing a singer to read an unfamiliar melody.

In music, neumes are written on a 4-line staff, both on the lines and spaces, and they were used in Western & Eastern musical notation prior to the invention of the 5-line staff notation. (the word comes from the Greek word for breath indirectly) They are used in Byzantine music, Slavic chant, Gregorian Chant, in some Spanish music, in Buddhist chant.

In the 14 century in Italy, colors were used - staff lines were red, clef signs and text were black. Other colors in other countries.

Suffice it to say they are "musical notation" used in sheet music to represent aurally perceived music through the use of ancient or modern musical symbols.