Active cables - any cable that has active components (components that need power to be provided to operate) as part of the cable, connectors, etc.
Passive cables - any cable that does not have active components as part of the cable, connector, etc
Active components could include Transistors (i.e. FETs), opamps, vacuum tubes, etc
Examples of active cables for microphones: - Schoeps KC5, KCY, nBob's, DPA d:dictate series, New Neumann KM A/D series LC4 cable
Examples of non-active extension cables for microphones: Neuman KM100 series cables, MBHO 603 cables, Schoeps vintage CMMT cables, Sennhieser MKH 8000 series extension cables