The term K Band is used in communications as well as astronomy and refers to different ranges. For astronomy, it refers to a Photometric System Passband centered on 2.2 microns (2190nm) or 136 THz within the Near-infrared range, with a Full Width At Half Maximum of 390nm. K may indicate the band or a filter adhering to the specification.
The letter is also used to indicate the Magnitude of the signal observed through the filter, e.g., citing "K = 1.5".
European Southern Observatory Very Large Telescope (ESO VLT)
Hawaii K-Band Galaxy Survey
Tully-Fisher Relation (TFR)