What is meant by the balance-of-payments?  Why does the balance-of-payments statement "balance"?

What economic transactions give rise to the receipt of dollars from foreigners? What transactions give rise to payments to foreigners?

The balance of payments is the record of monetary or economic transactions that happen between the residents of one nation and other nations across the globe within a given period, normally one year. 

The balance of payments statement balances since it makes use of the double-entry bookkeeping system whereby every credit entry is actually balanced by the debit entry. 

The economic transactions that give rise to receipt of dollars from the foreigners include:

1. Merchandise exports
2. Income from investments abroad (foreign investments)
3. Transportation travel receipts
4. Gifts received from the foreign residents
5. Transfers or aid obtained from the foreign governments/nations
6. Investments in the United States by the foreign residents.
7.  

The economic transactions that give rise to the payments to the foreigners include:

1. Merchandise imports
2. Income from investments in the domestic country, for example, the U.S. by the foreigners.
3. Transportation travel payments, for example, when domestic residents travel to other nations.
4. Gifts given to the foreign residents by the domestic residents.
5. Transfers or aid given to the foreign governments/nations
6. Investments in foreign nations by the domestic residents (U.S. residents).

Step-by-step explanation

The balance of payments is the summary of economic transactions of a country with other countries across the world. In other words, the balance of payments is the record of monetary or economic transactions between the residents of one nation and other nations across the globe which happen over a period of one year. The transactions entail exports and imports of services and goods as well as other financial assets, and transfer payments such as foreign aid.  

The balance of payments statement actually balances since every credit entry gets balanced by the debit entry. In other words, the balance of payments statement balances since it makes use of the double-entry bookkeeping system whereby every credit entry is actually balanced by the debit entry, and thus, the balance of payments numerically must balance in overall. 

The transactions of a country are categorized into receipts and payments. 

Receipts (also known as credits) simply arise from sale of services, assets, and goods to the foreign residents by the domestic residents, as well as from the gifts and transfers received from foreign countries. These transactions entail the exchange of the foreign currency for the domestic currency in the forex market. Thus, the economic transactions that give rise to receipt of dollars from the foreigners include:

1. Merchandise exports
2. Income from investments abroad (foreign investments)
3. Transportation travel receipts
4. Gifts received from the foreign residents
5. Transfers or aid obtained from the foreign governments/nations
6. Investments in the United States by the foreign residents. 

Payments (also called debits) basically arise from purchase of services and assets and goods by the domestic residents from the foreign residents as well as from the gifts together with other kinds of transfers to the foreign residents. These transactions entail exchange of the domestic currency(money) for the foreign currency (money) on the market for international currency (forex market). 

Therefore, the economic transactions that give rise to the payments to the foreigners include:

1. Merchandise imports
2. Income from investments in the domestic country, for example, the U.S. by the foreigners. 
3. Transportation travel payments, for example, when domestic residents travel to other nations. 
4. Gifts given to the foreign residents by the domestic residents. 
5. Transfers or aid given to the foreign governments/nations
6. Investments in foreign nations by the domestic residents (U.S. residents).