The animal the prince saw was probably a Malayan tiger, not a lion. There are no wild lions anywhere in Southeast Asia. But the name stuck, and over hundreds of years 'Singapura' became 'Singapore'.
Singapore today celebrates the story with a famous statue called the Merlion. It is half lion (for the name) and half fish (because Singapore was a fishing village before it became a busy city). The Merlion stands at the edge of the harbour, spouting water from its mouth.
Singapore is a tiny country - one main island plus around 60 smaller ones. The whole country is about the size of a single big-city region. You can drive from one end of Singapore to the other in under an hour.
Even though it is small, more than 6 million people live there. Many of them speak two, three or even four languages every day. Their families originally came from all over Asia, and that mix is part of what makes Singapore feel so special.