Hamilton proposed a financial plan to get America out of debt. He wanted to open a national bank and to put high tariffs on goods. Basically a government that would favor businesses. But Jefferson did not like this. He wanted a government that favored agriculture.
People were protesting the government's tax on whiskey, which was valuable to the livelihood of backcountry farmers. The government had to decide if they were going to undermine their own authority, or if they were going to ignore the cries of the people. but in the end, they decided to keep the tax.
During the French Revolution, America had realized that they were in the middle of a war between 2 allies. Hamilton wanted to support the British, because they had ties with them, and needed them to help pay off war debts. Jefferson, however, wanted to support the French, because he felt that not supporting an effort of freedom was an attack on liberty everywhere. But in the end Washington had to step in and decide to stay neutral.