What is language of repeat(L) = {ww | w ∊ L}?
$repeat(\cdot)$ is an operator on languages. It takes as an input a language $L$, and outputs a language defined by $\{ xx \mid x \in L\}$. That is, for any word $x\in L$ the string $xx$ will be in the output language $repeat(L)$.
A Few examples:

$L=\{ 0,00, 11\}$  =&gt;  $repeat(L) = \{ 00,0000,1111\}$
$L=\{ \}$   =&gt; $repeat(L) = \{ \}$
$L=\Sigma^*=\{\epsilon,0,1,00,01,10,11,...\}$ =&gt; $repeat(L)= \{\epsilon, 00,11,0000,0101,1010,1111,...\}$