What is the use of Delta symbol in set theory?

The $\Delta$ in set theory is the symmetric difference of two sets.

$A$ $\Delta$ $B$ $=$ $(B-A) \cup (A-B)$

In the context of elementary set theory the symbol $\triangle$ usually denotes the operation of symmetric difference of two sets: if $A$ and $B$ are sets, $$A\mathrel{\triangle}B=(A\setminus B)\cup(B\setminus A)\;.$$

This definition explains the name symmetric difference: we take both the set difference $A\setminus B$ and the set difference $B\setminus A$ and then form their union, so that the operation is commutative:

$$A\mathrel{\triangle}B=B\mathrel{\triangle}A\;.$$

You ought to prove to yourself that

$$A\mathrel{\triangle}B=(A\cup B)\setminus(A\cap B)\;;$$

this is even sometimes used as the definition of $A\mathrel{\triangle}B$.

In plain English, $A\mathrel{\triangle}B$ is the set of things that belong to exactly one of $A$ and $B$.