This is a great question. The challenge with this definition is that it is merely descriptive. It is a very useful definition in every day life for talking about science, but some questions are rather difficult to answer if one is using this definition:
- Am I following the scientific method?
- Assuming I have a specific goal in mind, does the scientific method help me achieve it?
- Is science good?
- I have been introduced to some concept (like faith healing), and they make a claim that their theories are backed by science. Are they speaking accurately?
These are important questions, but they are hard to answer with a 2-line definition like Google provides. They require digging deeper into what the scientific method means, and that is where we start to see the vagueness.
A method of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.
When I talk with people about science, the testing and experimentation sides of the discipline are what everyone tends to focus on. There's plenty of systematic observant methodologies out there, but we tend to think of the testing an experimentation process as the defining aspects of science. But that process has shifted over time. The idea of what it means to do an experiment and test hypotheses has changed since the 17th century.
Early science was dominated by inducitivism. Inductivism was primarily built around using induction to go from a small number of observations to a universal law. It had its process of affirming and denying these inductive leaps, but it was more "free range" than we typically think of science today. Positivism restricted it a bit, focusing on models which are predictive, but it had a ways to go to reach what we consider science today.
One of the more important shifts came Karl Popper in the early 20th century. Popper promoted the idea of falsification. Under Popper's thinking, you could make any claim you wish in science, so long as it was falsifiable -- there had to be a way to disprove one's statements. If I claim "all swans are white," that statement is falsifiable by observing a single black swan.
In my opinion, Popper's science is what most people think about, but he wasn't the last philosopher to touch it. One of the problems with Popper's approach is that scientific observations increasingly became statistical in nature. And, in statistics, it is virtually impossible to truly falsify anything. That left Popperian science in a bit of a limbo.
Thomas Kuhn provided the most successful follow-on to Popper's approach to science. Kuhn's definition of science included the scientific community itself, not just the experiment. He argued that science works in waves. There's periods of order where we're simply beating down statistical errors getting closer and closer to Popperian falsification, and then there's tumultuous periods of excitement where a bunch of theories get disproven and new theories (with less evidence behind them) come up in their wake.
All of these approaches to science are substantially different, and that's where the vagueness comes from. And, if one wishes to push the concept of science further back than the 17th century, we find we have to have even wider definitions of the scientific method which start bordering on guess and check. We start seeing definitions that accept more and more of what we now call pseudo-science. And that's okay! That's the fun of working with definitions!