transcriptional activation domain
If the DNA-binding domain is the part of a transcription factor that knows where to stand, the activation domain is the part that, once standing there, waves its arms and shouts 'over here — start copying this gene!'. It is the working hand that reaches out and recruits the heavy machinery of transcription to the spot.
Concretely, the activation domain is a separate region of the transcription factor that, while the binding domain anchors the protein to its DNA site, makes contact with other proteins: the Mediator complex, components of the general transcription machinery, and chromatin-modifying enzymes that loosen the DNA's packaging. By touching these and tugging them to the gene's promoter, the activation domain raises the chance that RNA polymerase will start, and how often. Curiously, many activation domains have no fixed shape on their own — they are floppy, low-complexity stretches that only fold up when they grab a partner, and they often work better the more of them you have (several weak activation domains stacked up beat one strong one). This looseness is a feature: it lets one activation domain make sticky, transient contacts with many different partners.
The split between binding and activation is one of the deep design principles of gene control. Because the two domains are physically separable, an activation domain fused to any DNA-binding piece will activate whatever gene that piece points to — the basis of the two-hybrid assay used to detect protein partners, and of GAL4-based tools used throughout fly and yeast genetics. It also explains repressors as the mirror image: a repression domain, on a protein bound nearby, recruits machinery that shuts the gene instead. The verb lives in the activation (or repression) domain; the address lives in the binding domain.
Researchers fuse the activation domain of yeast GAL4 to a protein they are studying; if that protein meets a partner carrying GAL4's binding domain, the two halves reunite over a reporter gene and switch it on — the classic yeast two-hybrid screen for protein interactions.
The verb of a transcription factor: a part that recruits machinery, separable from the part that finds the gene.
Many activation domains are intrinsically disordered — they have no stable structure until they bind a partner. This is normal and even useful, not a flaw; structured 'folds' are not required to do real biological work.