What is p(Evidence) exactly in a bayesian model? I'm having a hard time intuitively understanding what this means in a machine learning context. When using the variables $A$ or $B$ or some trivial example, it all makes sense, but when looking at machine learning formulas where there are real variables its harder to see exactly what is meant. For example, if $t$ is what I am trying to predict and $x$ is the training example or input...
$$
p(t|x) = \frac{p(x|t)p(t)}{p(x)}
$$ 
What is meant by $p(x)$? if $x$ is a training example, does it mean the probability of seeing $x$ out of all possible training examples (kind of like the probability of drawing $x$ from a hat)? the probability of seeing $x$ out of the previously known distribution of examples? or something else?
Sometimes I see this with model parameters such as $\theta$ as well which raises the same sort of questions.

Well, if you have the joint probability $p_{X,Y}(x,y)$, then $p_X(x)=\sum_y p_{X,Y}(x,y)$ is a marginal probability.
$p_{X|Y} = ( p_{Y|X} * p_X ) / p_Y$ has the form
Posterior = ( Likelihood $*$ Prior ) /  Evidence.
