In practice, a second passport can radically change your visa situation. The most important thing is visa-free entry to dozens of countries that previously required a complicated visa. For example, citizens of Chile, Israel, and EU countries can enter the US under the ESTA program without visiting the consulate. A passport from Romania, Lithuania, or another EU country opens the door to the Schengen area, Canada, Australia, and the UK. A Turkish passport is not as powerful, but it allows you to quickly and easily obtain electronic visas to many countries in Asia and the Middle East.
The second important advantage is the simplification of the visa procedure itself: fewer documents, faster processing, and fewer refusals. In addition, it becomes possible to apply for a visa from another country using a second passport, which is especially convenient for long stays abroad. Finally, it is a backup option: if the first passport stops working for some reason — political situation, sanctions, loss of visa validity — the second document saves the day.