just getting started in Signal Processing - easy question
The symbol $z^{-1}$ refers to a delay of one sample interval, no matter how long this interval actually is. It comes from the $\mathcal{Z}$-transform: if $X(z)$ is the $\mathcal{Z}$-transform of a data sequence $x[n]$, then $X(z)z^{-1}$ is the transform of the delayed sequence $x[n-1]$.

The transfer function (i.e. the quotient of the $\mathcal{Z}$-transforms of output and input sequences) is given by

$$H(z)=\frac14\left(1+z^{-1}+z^{-2}+z^{-3}\right)\tag{1}$$

which in the time (sample) domain means that the output sequence $y[n]$ and the input sequence $x[n]$ are related by

$$y[n]=\frac14\left(x[n]+x[n-1]+x[n-2]+x[n-3]\right)\tag{2}$$

This is of course the average of the current and the past three data samples. If, as in your example, all data samples have the value $8$, then the output is

$$y[n]=\frac14\left(8+8+8+8\right)=8$$