This is the inverse function of $a^n$. Hence $\sqrt[n]a$ means, you look for a number $b$, which when multiplied $n$ times with itself results in $a$.
For instance: We know that $2^3 = 8$, so $\sqrt[3]8 = 2$, $\sqrt[5]{-1}=-1$ because $(-1)^5 = -1$. $\sqrt[4]3 \approx 1.31607$ because $1.31607^4 \approx 3$.
If there is no number at the top of the root symbol, it means $n=2$, so $\sqrt[2]a = \sqrt a$.