In mathematical mode characters are spaced as if they were part of a single word, regardless of the actual space you insert. This article explains how to insert spaces of different lengths in mathematical mode.
Contents 
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
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.
Note: to see a description of the align*
environment see Aligning equations with amsmath
Spacing around operators and relations in math mode are governed by specific skip lengths:
\thinmuskip
(by default it is equal to 3 mu)
\medmuskip
(by default it is equal to 4 mu)
\thickmuskip
(by default it is equal to 5 mu)
For relationnal operators, such as < , > and =, LaTeX establishes \thickmuskip
space. But for binary operators such as +,  and x, the \medmuskip
space is set. The difference is almost unnoticeable.
You can force the spacing used in binary or relational operators, so you can define your own.
The previous example sets a particular spacing before and after #
by using \mathrel
(relational) and \mathbin
(binary) commands.
Description of spacing commands
LaTeX code  Description 

\quad 
space equal to the current font size (= 18 mu) 
\, 
3/18 of \quad (= 3 mu)

\: 
4/18 of \quad (= 4 mu)

\; 
5/18 of \quad (= 5 mu)

\! 
3/18 of \quad (= 3 mu)

\ (space after backslash!) 
equivalent of space in normal text 
\qquad 
twice of \quad (= 36 mu)

For more information see