When you say, "I did X once", that can mean, "I did X at some time in the past", or "I did X exactly one time."
The phrase is often used in the first sense to introduce a subject. Like, "I went to Chicago once," followed by an account of what you did there. In that case it doesn't necessarily mean that you only did it one time. You are just bringing up one particular time that you did it.
It's a fairly common joke to say, "I did X once" as if you were about to use it in the first sense and go on to describe a particular incident, and then just stop, thus converting the meaning into the second sense, I did this only one time. Or sometimes make some comment following up on the idea of it being only once. If it's an activity that people would expect you to do more than one time, this might potentially be funny if the line is delivered well. "I went to work once. I decided I didn't like it." Etc.