Carl spent much of his life fixated on the possibility of extraterrestrial life. Part of this was due to the “Drake's Equation”, that is, an equation that attempted to mathematically quantify the factors that might lead to extraterrestrial civilizations within our galaxy. From it, many came to conclude that, for all the billions and billions of stars in our galaxy, enough of them have planets, and enough of those planets must be suitable to life, that it would be statistically more likely to win the lottery than for there not to be life in this galaxy.
Indeed, it was some of his research that resulted in proving that amino acids—necessary for life as we know it—can be derived from basic compounds by the very radiation we find in space. This and other research pioneered the field of exobiology, that is, the scientific study of life outside of Earth. He helped found SETI, the famous Search For Extraterrestrial Intelligence program, and served on the board of trustees for a number of years. On many of the space missions that he helped plan, he helped assemble messages to attempt to make contact with potential alien lifeforms on their travels, from physical plaques on space probes to radio messages from Earth into the vastness of space.
All in all, Sagan was largely responsible for opening the doors to studying the possibility of life on other planets, a thought that was popular amongst lay people but often disregarded by scientists and other academics.