P(x|θ): direct probability
It gives the probability of contingent events (i.e. observed data) for a given hypothesis (i.e. a model with known parameters θ)
L(θ)=P(x|θ): likelihood
It quantifies the likelihood that the observed data would have been observed as a function of the unknown model parameters (it can be used to rank the plausibility of model parameters but it is not a probability density for θ)
P(θ|x): inverse probability = posterior probability
Starting from observed events and a model, it gives the probability of the hypotheses that may explain the observed data (i.e. of the unknown model parameters)