The “Ultras” was a term used as a name for the most extremely partisan members of the Federalist Party in the late 1790s. These were the people who were most strongly in favor of a war against France and who strongly supported the creation of the Alien and Sedition Acts.
In the mid-to-late 1790s, there was a major crisis in world affairs. The French Revolution had just occurred and many of the nations of Europe were fighting against France. They feared the new French political system and they feared that the French would try to impose their system on other countries through conquest. The United States got caught up in this war.
An early crisis for the United States occurred when France announced that its navy would stop American ships from trading with Britain. This was extremely damaging to the US economy, particularly to the economy in the Northeast. This region was the main stronghold of the Federalist Party. The Federalists’ economic interests, along with their ideological opposition to the French Revolution, led them, and particularly the Ultras, to demand a war with France.
At the same time, the Ultras were worried about domestic politics. They felt that the Democratic-Republicans were traitors for opposing the government and supporting the French. We must remember that power in the US government had never yet changed hands from one party to another and so it was still possible to think (for some, at least) that political opposition to the party in power was treason against the country. Because of this, the Ultras pushed for passage of the Alien and Sedition Acts, essentially banning criticism of the government.
The Ultras, then, were the most partisan and hardcore of the members of the Federalist Party in the late 1790s.