Norm
{ \left\| z\left( x \right) -e \right\| }_{ 2 }^{ 2 }
|| in mathematical notation means matrix norm. The number on the right bottom means p-norm. In the above example, it's a 2-norm or L2 norm. The 2 on the upper right means square.
Reference
http://mathworld.wolfram.com/VectorNorm.html
http://mathworld.wolfram.com/MatrixNorm.html
https://mathtrain.jp/lpnorm
https://scicomp.stackexchange.com/questions/2822/what-norm-to-choose-when