In hypothesis you want to test some statement about the real world, e.g. the average length of all men is 1.75m. We would then formulate a hypothesis test like e.g. $H_0: \mu_L=1.75$ versus $H_1: \mu_L \ne 1.75$.
This is our statement and we want to test whether in the real world this is a fact. But frequentists state that in the real world this is either true or false. As in the real world $H_0$ is either true or false, this means that in the real world $P(H_0=TRUE)$ is either 0 or 1.
So in theory the result of our hypothesis test should be $H_0$ is true or false but as we only work on a sample we can not make such hard conclusions, therefore we try to use some statistical variant of a mathematical technique called 'proof by contradiction'. For detail see What follows if we fail to reject the null hypothesis?.
For a thread on p-values see Misunderstanding a P-value?
Baysians do something different; they express their belief or credibility they have in their conclusion of the test, so it is not realy the probability that $H_0$ is true, but more the degree of belief they have in their conclusion they make after the test about $H_0$. This is why it is called ''credibility''.