What's the Root of Deportation?
In the United States, compared to many countries, we are fortunate enough to have a reasonably good quality of life, stability, a well-built, developed education system for all, a healthy economy, relative safety and lots of opportunities. This is not the case in many other nations.
In some countries the economy is such that many people don't have jobs and live in poverty. The education system may be lacking. There may be dangerous conditions such as wars or human rights violations. Citizens of such nations may want to move to a more developed or safe, stable nation such as the U.S. because they want a better life.
However, the U.S. limits the number of people allowed to move here and there are lots of costs and rules and requirements that people need to meet to even be considered. Some people find ways to get into U.S. even though they have not gone through the process of getting formal permission from the U.S. government to come to the U.S. Other people go through the formal process and receive permission to stay for just a little while but then they do not leave when they are supposed to leave.
Once a person is here in the U.S. without permission, unless the person's immigration status can be changed somehow, there is a risk that he or she will be found out and be made to leave the U.S. This remains true even if the person has lived here for many years and has a job, a home, a marriage and children who were born here in the U.S.
To understand why your parents came to the U.S., ask them. This is definitely an important part of the communication that should happen about deportation, and it may give you more insight into their life and story.