Why is nucleus called the brain of the cell?
The nucleus stores DNA, which is the code for building the proteins that carry out all the functions of your body.
The nucleus is called the "brain" of the cell because it holds the information needed to conduct most of the cell's functions. Other molecules make proteins from that information on a regular basis - each moment of our lives.
Proteins, specifically enzymes, carry out almost all of the activities of the cell - like making ATP energy from glucose in the mitochondria, moving substances across the cell membrane, and countless other jobs needed to keep a cell running properly.
These proteins are built by the cell using the information in DNA, which is held in the nucleus. So, say your intestine's cells need to break down the food you just ate - the DNA in the nucleus will be accessed to get the information needed to make the enzymes that will break down that food. In this way, the nucleus, much like a library, is constantly being accessed to use this information.