[fela]

I like to split the theorem in the following way:

P(Hypothesis|Data) = P(Hypothesis) * evidence_factor

P(Hypothesis) is the prior probability of the Hypothesis being true, in other words the probability we gave to the Hypothesis before seeing any of the data we are using in the theorem. When new data is observed, we use Bayes' theorem to update our believe in the hypothesis, which in practice means multiplying our prior probability by a number that depends on how well the new data fits our hypothesis. More precisely:

evidence_factor = P(Data|Hypothesis)/P(Data)

So it is the ratio of how likely our data is if our hypothesis is true, compared to (divided by) how likely it is in general. If it is more likely to occur in our Hypothesis, our probability of it being true increases, if it is more likely in general (and thus also more likely in case our hypothesis is not true, you can prove mathematically that those two statements are the same), then our believe in the hypothesis decreases.

TLDR: Prob(Hypothesis after I have seen new data) = Prob(Hypothesis before I saw the new data) * (how likely I am to see the data if my hypothesis is true, compared to in general)