The meaning of symbols
$x$ and $y$ are elements of a set $S$. For example, if $S = \{1, 2, 3\}$, we can select $x = 1$ and $y = 2$. 

EDIT:
As pointed out by David below, $*$ could be multiplication or convolution, it's hard to tell from the context. 

$\in$ means 'in', that is, that $x$ and $y$ are in a set. We can write 'x and y are elements of the set $S$ ' in math as: 

$x, y \in S$

Again, following my example, that would be $1$ and $2$ are in the set $\{1, 2, 3\}$.

$\forall$ is verbalized 'for all'. It means for every element in the set, something is either true or false. For example:

$\forall x \in S, x &lt; 5$ means that all of the elements in my set $S$ are less than 5.

$I$ is the identity function. 

The entire phrase $I: \forall X.  X \rightarrow X$

(EDIT: removed example, as it was misleading)

means the identity function preserves the value of the variable $X$. More concretely, $I$ is the function that maps $X$ to itself. For all values of X, the output of the function is X.

Hope that helps!