A course has 1 or more attempts, which is an attempt to take and pass the entire course.
A quiz has 1 or more attempts, which is the act of taking the quiz. A quiz attempt happens in the context of a course attempt. You can re-attempt a quiz as often as you want in a course attempt, up to the maximum number of permitted attempts for the quiz.
So, if a course has 3 attempts, and a quiz in that course has 4 attempts, you could theoretically take that quiz up to 12 times, if you attempted the course all 3 times and took the quiz the maximum number of times.
The default number of attempts for a quiz or for a course is 1, however.
In a case of a quiz with one attempt, you only have one attempt at it, period.
Leanpub will warn you if you are about to attempt the final (or only) one of your quiz attempts.
Please note that there is no limit on your access to the course material itself. You can still access the course material even after you have completed all the course and quiz attempts.