Answer:
The nucleus contains the DNA of the cell which can be thought of as the brain of the cell.
The nucleus responds to stimuli via receptors which can be primary or secondary. Basically, an external ligand (hormone, protein, nutrient, etc) binds to the surface receptor of a cell, this, in turn, causes the receptor to release a messenger (most of the time circular AMP (cAMP)) which binds to a secondary receptor which is either directly inside the nucleus or on the nuclear envelope. Finally. the portion of the DNA which is responsible for the protein to respond to the ligand is activated and begins transcription.
The activated DNA section (gene) produces mRNA which in turn produces a protein in response to the ligand.
On top of this, the entire cell cycle of rest, growth, and division is controlled by the nucleus.