1310 nanometres is the wavelength of light first used in fibre-optic cables to transmit data between sites. AT&T used 1310nm lasers to illuminate single-mode fibres for the long-distance interconnections between sites driving adoption of the 1310nm wavelength in telecoms consciousness. You also need to have a detector to act as the receiver at the other end of the link. In this case, photo-diodes tuned to a particular wavelength provide this. Receivers have a higher bandwidth (accepting colours from either side of the emitted stream) allowing them to operate with a range of sources. (Remember each source will be a slight variance around the ideal mixture to provide the light source. The wavelength refers to the typical colour that your emitters provide light.)
There are more wavelengths in use, with 850nm and 1300nm used to drive multi-mode fibres. Multi-mode fibres are now frequently using LEDs rather than lasers. Single-mode fibres typically carry 1310nm or 1550nm light. Initially, single-mode fibres used an 850nm light source, but this needed a much narrower fibre core (~5μm as opposed to the ~9μm today). Manufacturing tolerances made the earlier narrower fibre much more expensive.
A Gallium Arsenide semiconductor laser diode generates the light. The level of chemical ‘doping’ in the silicon controls the specific wavelength of light emitted. The first of these semiconductor laser diodes was developed by General Electric research, under a team led by Robert N. Hall in 1962.