In ${\mathbb R}^n$, a "reasonable" $n$-dimensional set $S$ is typically defined by inequalities of the form $f_i(x_1,x_2,\ldots, x_n)\geq0\qquad(1\leq i\leq r)\ ,$ i.e., is defined as $S:=\bigl\{{\bf x}\in{\mathbb R}^n\ \bigm|\ f_i(x_1,x_2,\ldots, x_n)\geq0\quad (1\leq i\leq r)\bigr\}\ ,\qquad (1)$ or is a union of sets of this kind. E.g., the full $n$-cube $C$ centered at ${\bf 0}$ with side-length $2$ is described as $C:=\bigl\{{\bf x}\in{\mathbb R}^n\ \bigm|\ -1\leq x_i\leq 1\quad (1\leq i\leq n)\bigr\}\ ,\qquad(2)$ and there is no essentially simpler way to describe $C$.
The descriptions $(1)$ and $(2)$ are "implicit". They give easily testable conditions whether an arbitrary given point ${\bf x}=(x_1,,\ldots, x_n)\in{\mathbb R}^n$ belongs to $S$, resp. $C$, or not.
If your set $S$ is more complicated than the cube $C$ you maybe want an explicit "production scheme" that produces each and every point ${\bf x}\in S$, hopefully exactly once, starting from a "standard set" like $C$ or a unit ball $B\subset{\mathbb R}^n$. Such a "production scheme" is called a parametric representation of $S$; it has to be set up ad hoc by means of "mathematical engineering", starting from the equations $(1)$ that define $S$ and using your mathematical expertise about the special functions appearing in $(1)$. In the end you have a hopefully injective map ${\bf g}:\quad C\to{\mathbb R}^n,\quad {\bf u}\mapsto {\bf x}:={\bf g}({\bf u})\ ,$ that produces for each point ${\bf u}=(u_1,\ldots,u_n)$ in your standard set (say, $C$) a point ${\bf x}=(x_1,\ldots,x_n)\in S$, and it is guaranteed that you obtain all points of $S$ in this way.