There are many reasons why Czechs decided to immigrate. The year of immigration could give you some important clues. Early immigration (1850-1900) is usually about the desire to farm and own one's land. Serfdom and Manors existed in the Czech lands until 1848. Even after that, land ownership was restricted to certain classes. It was a highly stratified society with not a lot of transfer between classes.
In the United States, there was lots of land available. Immigration agents in the United States sent glowing reports (overstated, exaggerated, borderline lies!) that made claims of fertile farmland for very cheap. Most Czechs immigrated in clusters. Many Moravian-Silesian Czechs immigrated to East Texas, in Fayette, Wharton, and Lavaca counties. Many Bohemian Czechs immigrated to Chicago, Nebraska, and Iowa. If your ancestor immigrated to more rural areas like Nebraska, Iowa, or East Texas, they were most likely a farmer. This means that a huge impetus for immigration could have been land ownership.
As the population of the Czech lands continued to grow, the amount of available land for farming became smaller and smaller as it was divided between more and more sons, until it became extremely difficult to eke out a living from farming, which is what the peasants had to do in order to survive. Also, the topography of the land in many places was not very conducive to farming. Picture rocky, forested hills. Most villages in the Czech Republic are clustered around streams. Farming was a difficult venture.
Immigration could also have been motivated by the desire to escape military responsibilities. The Austrian Empire had done little for the Czechs besides tax them. They did not even really protect them. There was no strong nationalistic allegiance that Czechs felt towards the Austrian Empire. Many of them were cynical of their political leaders. The German language became the language of education and government, and Czech was banned, which was not done willingly. Many Czechs felt that the required military duty for their sons was a bitter injustice, in particular during times of war. Many wondered why they should support a cause with their blood when it would give no tangible benefit to them. Instead of sending just their sons, many decided to travel together as families.
Czech protestants and Jews experienced religious persecution despite that both of these groups have long historical ties to the Czech land. In the late 18th and early 19th century, Czech Jews faced some extremely anti-Semitic persecution with laws that declared that only one Jewish boy per family was allowed to marry. This was an effort to decrease the Jewish population. Ironically, this led to a wider dissemination of Jews in the Czech lands when second, third, etc. sons left their hometowns for a neighboring village to marry.
In short, many Czechs desired freedoms that were to be had in the US that were impossible for them to acquire in their homeland; freedom to own land, freedom of political thought, and freedom of religion.
Many immigrants to America were of the middle of the peasant class. They had both the means and the motive to leave. Many of these were "hausler" (hired hands who did not own their own land, but were paid in food, clothing, and shelter.), "passekař" (people who cleared an area of hillside of its trees in order to farm on it. The plots for these people are usually very long and skinny. The terrain was usually rocky and not ideal for farming, but better than starving!), or "bauer" - farmers who owned or leased some land but could see no possibility of improving their situation. Those with occupations like miller, weaver, doctor, or those from the higher classes of clergy and nobility did not immigrate as frequently to the United States between 1850-1930, though it did happen.