Confusing language and terminology is a big part of what makes statistics confusing. Each Binomial Trial -- also known as a Bernoulli Trial -- is a random experiment with only 2 possible outcomes, called "success" and "failure". The Probability of a "success" (or a "failure") is the same every time the experiment is conducted. A simple example is a coin flip.
A "success" is defined as what we want to count. Let's say we are performing quality control in a manufacturing process. We are counting defects. Every time we find a defect, we add 1 to the count of "successes".
I always found that confusing. So in the book -- instead of saying "success" or "failure" -- I suggest saying "yes" or "no", and count the yesses.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.