If you don't already have knowledge of the period, you might look for a timeline of key events in the 19th century. You'd find a couple things related to this question:
In the German states and elsewhere in Europe in 1848 there were a number of revolution movements, trying to replace old conservative governments. The revolutions had a more liberal flavor (wanting parliaments and such). Some also had a strong nationalist flavor -- in Germany, that meant creating a united Germany. But the revolutions failed, and many of those who wanted to see change in the German states left and went to the United States. I live in a town where many of them showed up!
As for Ireland, from 1845-1849 there was a devastating famine. Ireland had depended on the potato as its chief crop and food source. When a disease struck the potato plants, famine conditions became awful -- and governments did little to help. Many Irish people left, hoping to find new lives in America.
