eukaryotic gene regulation: \\ Transcription factors are sometimes activated by phosphorylation...

There are different types of hormones. Some are protein hormones, some are steroid hormones. Steroid hormones can directly enter the cell crossing the plasma membrane and bind with the intracellular receptor for carrying out further changes. But protein hormones mostly bind with the receptors present in the cell membrane and activates a signaling cascade which results in translocation of the transcription factor in the nucleus. The transcription factor facilitates transcription of the target gene and increases the expression of a protein which brings out further changes.

If you think about Growth Hormone (GH) in our body you will find that GH binds with the GH-receptor and activates a MAPK signaling cascade where there is consecutive phosphorylation of different substrates and which finally results in phosphorylation of the transcription factors and this facilitates translocation in the nucleus to increase the expression of target genes.