When you tell a story, it's common to talk about how things changed from the beginning to later on. To do this, you can use "At first...":
I saw something out on the ocean. At first, I thought it was a piece of trash or something. Then I noticed that it was moving. Suddenly, my heart froze as I realized that it was a shark's fin.
So "at first" explains what was happening before things changed.
You can also put "at first" at the end of a sentence:
He seemed nice at first. But as the relationship went on, he started to get more and more jealous.