An additive white Gaussian noise, or AWGN, channel models the received signal as

$$Y(t)=X(t)+N(t),$$

where $X(t)$ is the transmitted signal and $N(t)$ is noise.

Additive means the disturbance is summed with the signal rather than changing it multiplicatively.

White means the noise has a flat power spectral density over the idealized frequency range.

Gaussian means every finite linear combination of noise sample values is normally distributed.

The three assumptions are logically separate. A channel can have additive non-Gaussian noise, colored Gaussian noise, or other impairments entirely.

AWGN is useful because filtered thermal noise is often approximately Gaussian and nearly spectrally flat over the bandwidth of interest. It provides a tractable reference channel for comparing modulation, detection and coding schemes.