From the wiki page:

Ulster Says No was the name and slogan of a unionist mass protest campaign against the provisions of the 1985 Anglo-Irish Agreement which gave the government of the Republic of Ireland an advisory role in the governance of Northern Ireland.

Page here if you want some more reading.

As I recall (and I was young at the time so this may be wrong) it got rolled out for various other stuff.

Catchy slogan in fairness.