The cathode of a diode (including an LED) is the n-side of a PN junction - it is generally considered to be the side where current coming out from. In a diode, current flows from the cathode but not back in, and is denoted by the flat, vertical portion of the arrow/line symbol.
Except in the case of Zener diodes, when biasing a diode, you always assume that the cathode is negative. Even if the positive voltage is on the cathode side of the diode, then it will be considered a "negative voltage" when writing out the equations to describe the circuit.
The n region of a diode.
Electronic Devices : Conventional Current Version, 9th Edition by Thomas L. Floyd
The n side of the diode is called the cathode.
Grob’s Basic Electronics, 11th Edition by Mitchel E. Schultz