I have trouble translating Turing machine language, can you help me break down language notation to English?
When $s$ is a symbol and $n$ is a natural number, "$s^n$" means "$s$ repeated $n$&nbsp;times".  So you're being asked to recognize the language of all strings that consist of $n$&nbsp;zeros followed by $n$&nbsp;ones, for any possible value of&nbsp;$n\geq 0$.  That is, $\{\epsilon, 01, 0011, 000111, 00001111, \dots\}$, where $\epsilon$ denotes the empty string (some people write $\lambda$ for the empty string, instead).