If DNA is placed in a gel containing an electrical gradient, it will migrate toward the positive end. DNA is negatively charged because of its phosphate backbone. Protein bound to the DNA will slow its migrations due to increased friction and charge neutralization. Attachment of specific DNA sequences to a solid support, allows for the purification of DNA binding proteins. In general, to figure out how a protein works, it is often necessary to isolate the protein so that you know that whatever you are observing is due to that protein and not some other protein.
Activators are modular in structure.
One part of the activator binds DNA, and another part binds and recruits the transcription machinery. The DNA binding domain and the activation domain are coded for on separate parts of the same gene. The DNA binding domain and the activation domain fold into distinct structures. By recombinant DNA techniques, the individual domains can be made separately or swapped with other DNA binding and activation domains. If you change the DNA binding domain you also need to change the DNA binding site.