Now for what he is known for. The second Voyage. That voyage was Cuba to Mexico. It was a really short trip across the Gulf of Mexico. Before he left Cuba, his voyage was canceled by the goverment. Hernando ignored it and went to Mexico anyway. When he got their, there where already people there. They're called the natives.
Hernando didn't want them there. He decided to have a war with the natives. He was able to win the war. He got the land, and built a new city. A great city which lasted years. It was a nice peaceful city. Anyway, Hernando was a governer of Mexico, which they called New Spain.
Remember when I said that New Spain was peaceful, it wasn't for so long. The Aztecs came for war. It was the most dangerous war in the history of Mexico. Hernando fought very hard in the war. Luckily Hernando was able to win the war for Mexico. That is what he is known for. Sadly he later died from illness.