There are numerical limits on the number of immigrant visas that can be granted to aliens form any one foreign country. This limit is the same for all countries. The limit is based on place of birth, not citizenship. Where the immigrant is "charged", means that person is counted towards a given country's numerical limit. For example, an immigrant born in Ethiopia is "charged" to Ethiopia, and therefore counted towards reaching the numerical limit for that country. The person would be "charged" to Ethiopia, even if the immigrant born in Ethiopia was born of Yemeni parents and has a passport from Yemen.
Although immigrants are normally "charged" to their country of birth, and immigrant is sometimes able to claim another for the sake of immigration. You would do this if it helps the immigrant in reaching the "cut-off date" date faster. For example, suppose you were born in India, but your spouse was born in Sudan. The "cut-off date" for a person born in India is earlier in family fourth preference immigration category than the "cut-off date" for a person born in Sudan. We can "charge" you to Sudan, rather than India, and you can use the more favorable cut-off date for Sudan. Therefore, you would be able to immigrate years earlier with a chargeability to Sudan than a chargeability to India.
Source: U.S. Department of State.