Why "Linear" means the output is a scaled copy of the input: doubling the input voltage doubles the output voltage, so the waveform shape is preserved. This matters for modes whose amplitude carries information, such as SSB and AM, since any distortion creates harmonics and intermodulation products that splatter into adjacent frequencies. Class A, AB and B amplifiers are used for linear service; Class C is deliberately nonlinear.
Watch out The Class C choice is the opposite case: it conducts for less than half the cycle, is very efficient but badly distorts the envelope, so it suits only constant-amplitude modes like FM and CW, and its rich harmonic output is exactly what makes it useful as a frequency multiplier.
Linear = faithful copy, just bigger. Class C is efficient but ugly, fine for FM/CW, never for SSB.