A common example in CFG is the palindrome example. These examples often contain the $\ ww^R$ notation for the string.
An example from my class could be:
Strings $\ ww^R$ over the alphabet $\ \Sigma = \{0,1 \} $ (a subset of palindromes over $\ \Sigma $), or
$$\ L=\{ww^R ｜ w = (a + b)^+ \}$$
My confusion lies in the notation $\ w^R $, i don't understand what the purpose of this is.
$w^R$ is simply the string $w$ reversed. For example, if $w = abb$, then $w^R = bba$. It is easy to see then that the strings of the form $ww^R$ are exactly the palindromes, such as $abbbba$.