Scientific method was important to it's time period because it is the basis of thinking outside the box and thinking logically. For example, a hypothesis is found then answered with research, instead of praying to god for a solution to the problem.
England was one of the most influential countries in the renaissance because at that time it was a monarchy. That meant the king didn't want people to know more and progress. This challenged Francis Bacon to go against the king and try to improve the knowledge of the people.
When Francis Bacon said a man who begins in certainties will end with doubts he meant that if someone was certain that god will give them the answer then they will end up not knowing the real answer, but if a man starts with doubt and answers his question with critical thinking (like scientific method) he will end with the true answer to his question.
That is an example of humanistic thinking so it shows humanism.
Scientific method is still used today, it used in almost every science experiment and theory. For example, when we do a lab in science the first thing you do is find a hypothesis then try to prove it with data from an experiment. That is using scientific method.