Citizenship in the United States means being a citizen of the United States.  A person who has citizenship is called a citizen. Citizenship does not just mean that a person lives in the United States. United States citizenship gives people many rights, many protections, and also some duties.

Types of citizenship
There are two ways that people can become citizens of the United States.

The first is called "birthright citizenship."  Anybody who is born in the United States automatically becomes a United States citizen.

The second is called "naturalization."  This is for people who were born outside the United States.  A person becomes a naturalized citizen if they apply for citizenship and are approved.

Once a person is a naturalized citizen, they have all of the same rights, protections, and duties as a person who was born in the United States.

What it means to be a citizen

Rights
Being a United States citizen gives a person many rights.  Here is a list of some of these rights.

 Freedom to live and work in the United States.  Once a person is a citizen, nobody can take away their right to live in the United States.  Nobody can make them leave the country.  The government cannot deport a citizen, like it can with non-citizens.
 Freedom to enter and leave the United States.  Citizens can leave the United States for any amount of time they want to.  They can always come back.
 Freedom to choose the government by voting.  Voting is free and secret.  Nobody can be told they cannot vote because of their race, ethnicity, skin color, home country, disability, age, gender, or the language they speak.  Citizens do not have to vote.

Duties
Citizenship also comes with duties.  Here are some of those duties.
 Jury duty.  Only citizens can serve on juries.
 Military participation (if needed). Citizens do not have to serve in the United States military.  As of 2016, the United States has an all-volunteer military.  However, in the past, the United States has used "a draft" to call people up to serve as soldiers.  This has not happened since the Vietnam War.  Still, male United States citizens have to sign up with the Selective Service System so they could be called up if there were a draft in the future.
 Taxes. All American citizens, including those who live in other countries permanently, must file a federal income tax report (called a "return"), even if they do not live in the United States.  United States citizens are taxed on their income no matter where in the world they live or earn that money.
 Laws and loyalty. When a person becomes a United States citizen, they take an oath that says they promise they will be loyal to the United States; follow the laws of the United States; and obey the Constitution.

Benefits and protections
 Consular protection while traveling in other countries. The United States has consulates, or embassies, in most other countries.  Their job is to help American citizens who have problems in those countries.  If a citizen is traveling in another country and gets arrested, they can ask to speak to someone from the U.S. Embassy.  The Embassy can give advice and may be able to help.
 It is easier to sponsor relatives who want to come to the United States: To get some types of immigrant visas (called IR and F visas), a person must be related to a U.S. citizen.
 Citizens' children become citizens even if they are born in other countries. Usually, if both parents are United States citizens, and their child is born in another country, the child automatically becomes a United States citizen.  If only one parent is a U.S. citizen, it depends on how long that parent has been in the United States.
 Protection from deportation. Once a person becomes a naturalized U.S. citizen, they cannot be deported.
 Protection from losing citizenship.  Once a person has United States citizenship, no one (including the United States government) can take it away from them, unless the person asks to give up their citizenship or gained naturalization illegally.

Renouncement of citizenship
Americans are permitted to formally abandon their citizenship, even if they do not possess another citizenship and become stateless as a result. Boris Johnson, Prime Minister of the United Kingdom, was an American citizen because he was born there.  He renounced his American citizenship in 2016.  5411 other Americans renounced their citizenship in the same year.

References

Other websites
 10 Steps to Naturalization: Understanding the Process of Becoming a U.S. Citizen (in Simple English)
 United States Immigration and Naturalization Service (official website about citizenship and naturalization issues)

Nationality
United States law