The main reason why so many people from Ireland migrated to North America during the 19th century was the event that is commonly known as the Irish Potato Famine. This was an event that began in 1845 and is commonly said to have ended in 1852.
At this time in Ireland, the peasantry was terribly poor. Most of the peasants subsisted largely on potatoes. These rural poor made up about half of the entire population of Ireland. In 1845, a disease hit the Irish potato fields. The disease killed large portions of the potato crop. Then it kept coming back. This meant that Irish peasants had to either leave the land or starve to death. Huge numbers of them left Ireland and migrated to North America.
Thus, the potato famine was the biggest reason for this migration.