To be honest, there are as many interpretations of Bayes' theorem as there are books about it. The one shown previously is the main one that we will be discussing. I would also encourage you to refer to https://brilliant.org/wiki/bayes-theorem/ for further reading.
To make this more concrete and formal, let's start off with a bit of intuition and formality; it will help us set the stage for what is to come.
When we use Bayes' theorem, we are measuring the degree of belief of something, the likelihood that an event will occur. Let's just keep it that simple for now:
The preceding formula means the probability of ...