A transcription factor is a protein that alters the transcription of DNA into RNA. It turns out that a lot of the regulation of gene function is at the level of transcription. So, if a bacterium needs more β-galactosidase in order to break down lactose, it increases the transcription rate of the β-galactosidase gene by altering the transcription factor that affects the rate at which it is transcribed.
A large portion of the human genome is dedicated to the control of the expression of genes that encode proteins that actually do stuff. Some of these control elements are transcription factors.
I will link nodes that reference specific transcription factors below. If you node any, /msg me and I will link it.