Time shifting a signal

Whenever a signal can be expressed in the form

$$y(n) = x(n-M),$$

$y(n)$ is a delayed (time-shifted) version of $x(n)$.

If $M$ is a positive number,

$$y(n) = x(n-M),$$

the shift on the time axis is to the right.

If $M$ is a negative number,

$$y(n) = x(n+M),$$

the shift on the time axis is to the left (the signal has been advanced in time).