The lower-left spiral consists of all the points $P(x,y,z)$ specified by the coordinate functions

$$\left\{\;\begin{aligned} x &= \cos(8\pi t)\\ y &= \sin(8\pi t)\\ z &= t\end{aligned}\right.$$ We speak of coordinate functions because the coordinates $x$, $y$ and $z$ are functions of the variable $t$. As $t$ increases from $-1$ to $1$, the point $P$ spirals counter clockwise in the upward direction, starting in $P_{-1}=(1,0,-1)$ and terminating in $P_1=(1,0,1)$.

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In general, you can describe a space curve mathematically by three functions

$$\left\{\;\begin{aligned} x &= f(t)\\ y &= g(t)\\ z&= h(t)\end{aligned}\right.$$ We speak of a parameterisation or parameter equations of the curve with parameter $t$. Almost always one uses neat functions $f, g$ and $h$ as coordinate functions. The parameter $t$ represents time in many applications.