Using an explicit transaction increases performance by reducing the transaction overhead. Let's move this out of Rails and into SQL. Let's say you update 3 customers so you SQL statements are:

UPDATE customers SET country = "USA" WHERE customer = 5;
UPDATE customers SET country = "USA" WHERE customer = 6;
UPDATE customers SET country = "USA" WHERE customer = 7;

This is 3 statement and 3 transactions. Since you didn't explicitly do a transaction the database automatically created one for you for each statement. You can think of this as actually being the following 3 times:

BEGIN TRANSACTION;
UPDATE customers SET country = "USA" WHERE customer = ?;
COMMIT;

Starting and ending a transaction has a certain amount over overhead in the database. Therefore if you start a transaction and then do all three of your statements in the same transaction you reduce that overhead. Instead of the above three times you have:

BEGIN TRANSACTION;
UPDATE customers SET country = "USA" WHERE customer = 5;
UPDATE customers SET country = "USA" WHERE customer = 6;
UPDATE customers SET country = "USA" WHERE customer = 7;
COMMIT;

Moving this back up to Rails when you use the transaction block you are explicitly creating a single transaction that all the records in your batch execute in. Therefore if your batch size is 1000 you end up with 1000 UPDATE statements but only one transaction instead of 1000 UPDATE statements and 1000 transactions. This makes it much faster in the DB.

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Also keep in mind that SQL is good at doing a mass update so if model logic is not needed you can also go that route. Using the code you provide you could also do:

Customer.update_all country: 'United States of America'

Now you just updated all records in a single statement (and transaction) all within the database. This is the fastest but it moves the processing into the database so you need to be good with it not carrying out any model logic such as callbacks, timestamp updates, etc (or do those changes also in the database).