Hypothesis testing first starts with theory. Theories are particular assumptions about the way things are. After a theory is formulated, a conceptual hypothesis is created, which is a more specific (than pure theory) prediction about the outcome of something. Next an experimental hypothesis is created. This is where definitions are operationalized so specific matters can be tested. For example, you could operationalize affection as number of hugs and kisses and other related actions. Then you statistically hypothesize in order to measure and test one of two hypotheses: the null, or H0, which represents non-effect (i.e. no difference between samples or populations, or whatever was tested), and an alternate hypothesis, H1.
The alternate hypothesis is that there is a difference, or an effect. It can be that one mean is greater than another, or that they are just not equal. So, the purpose of statistical testing is to test the truth of a theory or part of a theory. In other words, it is a way to look at predictions to see if they are accurate. To do this, researchers test the null hypothesis. We do not test the alternate hypothesis (which is what we think will happen). We do this because we base our testing on falsification logic (i.e., it only takes one example to prove a theory is wrong but conversely you cannot prove that a theory is right without infinite examples, so we look for examples where we are wrong).
The probability associated with a statistical test is assigned to the possibility of the occurrence of Type I error. This is the probability that you will reject the null hypothesis when in fact the null is true and thus should not have been rejected. It is saying there was an effect or a difference when there really was not.
The process of statistical testing can result in probability statements about the theories under consideration but only under certain conditions. Statistical testing and hypothesizing is representative of theory when it is conceptually (verbally and operationally) connected to theory. This means that there has to be a logical and direct association between the statistical probability statements and the theory in order for those statements to represent the overarching theory. This link is forged by the experimental and conceptual hypotheses.