Understanding Communication Theory Jargon for Statistical Linear Models
The equation $y =  hs + n$ is a discrete-time model of a certain kind of wireless communications system.


$s$ is a complex number, drawn from a finite set called a "constellation", that represents the information being transmitted.
$n$ is a complex, circularly-symmetric Gaussian random variable with zero mean and variance usually denoted by $N_0$.
$h$ represents the effect of the communications channel. In this simple model of a wireless channel, $h$ is a complex Gaussian random variable with zero mean and variance one. This model is called Rayleigh-fading because $|h|^2$ is a Rayleigh-distributed random variable.
$y$ is the received complex number. From it, the receiver must make an estimate of $s$. This estimate is usually calculated by first estimating $h$, and then finding $$ y' = \frac{h^* y}{|h|^2} = s + \frac{h^*n}{|h|^2} $$ Here you can see the importance of $|h|^2$ to enhance the noise, which is why the channel is called Rayleigh. The estimate of $s$ is calculated by finding the constellation element that is closest (in Euclidean-distance sense) to $y'$.