How is gene expression related to the central dogma of molecular biology?

The central dogma shows how information is transferred from DNA to RNA to protein; when the cell receives a signal that a gene must be expressed, RNA Polymerase is recruited to the region of DNA where that gene is located. It makes an RNA copy of that region of DNA, in a process called transcription.

This RNA is then transported out of the nucleus of the cell, and is "translated" into a protein by molecular machines called ribosomes. The process of going from DNA (gene) to RNA to protein is basically gene expression.