Spacing in maths mode is useful in several situations, let's see an example:
Assume we have the next sets \[ S = \{ z \in \mathbb{C}\, |\, |z| < 1 \} \quad \textrm{and} \quad S_2=\partial{S} \]
As you see in this example, a mathematical text can be explicitly spaced by means of some special commands
Spaces
The spacing depends on the command you insert, the example below contains a complete list of spaces and how they look like.
Spaces in mathematical mode. \begin{align*} f(x) =& x^2\! +3x\! +2 \\ f(x) =& x^2+3x+2 \\ f(x) =& x^2\, +3x\, +2 \\ f(x) =& x^2\: +3x\: +2 \\ f(x) =& x^2\; +3x\; +2 \\ f(x) =& x^2\ +3x\ +2 \\ f(x) =& x^2\quad +3x\quad +2 \\ f(x) =& x^2\qquad +3x\qquad +2 \end{align*}
Check the reference guide for a description of the commands.