What do $x\in[0,1]^n$ and $x\in\left\{ 0,1\right\}^n$ mean? $x\in[0,1]^n$ 
$x\in\{0,1\}^n$ 
Thank you in advance.

The first entry is an interval $ [0, 1] $ in the Reals raised to the power n. E. g. for n=2, you can think of this as the unit square. I.e. $ x \in [0, 1]^2 $ iff it is in the unit square
The second entry {0, 1} is simply the set containing only 0 and 1. Picturing our n=2 square from the fist example, this set describes only the 4 corners of the square. Therefore $ x \in \{0, 1\}^2 = \{(0,0), (0,1), (1,0), (1,1) \} $ iff it is one of the vertices of the square. 
Hopefully you can see how this extends to n in general.
