What is Math Mode

You enter math mode by typing a dollar sign $, and you leave math mode by typing another dollar sign $. You should take a look at Chapter 3 of The Not So Short Introduction to LaTeX

TeX knows several modes, two of them are math mode and display math mode. Typesetting of ordinary text such as words nor numbers is different compared to mathematical formulas or a mathematical identifier such as x, which should look different from the text x (it does differ here in this editor only vaguely)

In order to let TeX know which mode should be used, there are indicators to enter math mode:

• Inline math mode, being entered $ and closed with $
• Display math mode, used with an enclosing $$...$$ in plain TeX or with \[...\] in LaTeX
• Typing inside \begin{math}...\end{math} in LaTeX
• Several math environments in LaTeX enter the math mode automatically, such as equation, align, alignedat, gather etc.

Several characters/symbols being connected to math content require entering the math mode, such as \mathbb{R} etc.

I guess that an even better way to enter math mode is to use \( and \), as discussed in this answer.