I heard on the first episode of Cosmos that astronomer Giordano Bruno was punished because he believed there are other planets with life on them. The Roman inquisition sentenced him to execution because they thought this belief violated the fact that 'God's wrath is not eternal'. I would be appreciate it if you provide me a resource to read about it, or give me an explanation. I am not Christian and this idea is so new to me.
According to the program, Bruno was found guilty
of questioning the Holy Trinity and the divinity of Jesus Christ, of believing that God's wrath is not eternal, that everyone will be saved, of asserting the existence of other worlds.
To answer your first question, "What does it mean that God's wrath is infinite?" it appears, based on the quote from the program, that Bruno was a universalist. This was, and often still is by many Christians, considered a heresy.
The answer to your second question, "What is its relation to existence of life on other planets?" is that there is none. These were separate, distinct charges, unrelated to each other. There is no implication that the believing in other worlds is in any way related to the believing that God's wrath is not eternal.