The "Principles of 1798" was the slogan of the Democratic-Republican Party. The principles referred to are those championed in the Kentucky and Virginia Resolutions, which were written by James Madison and Thomas Jefferson who were both Democratic-Republicans.
Thomas Jefferson and James Madison wrote the Virginia and Kentucky Resolutions in response to the Alien and Sedition Acts of 1798, which included four bills empowering the federal government to fine and imprison persons advocating actions deemed dangerous to the Republic or refusing to follow federal law. In these resolutions, Jefferson and Madison argue that states have an intrinsic right to interpret a federal law as unconstitutional and not follow it.
The "Principles of 1798" became a slogan for the party during the 1800 election in which Jefferson won the presidency. He had most of the acts repealed but did use powers from the Sedition Act to imprison political opponents before letting it expire.