I read in Tortora and Derrickson that :
Enkephelins are 200 times powerful than morphine in their analgesic effects.
I wonder how exactly researchers arrive at a number (like 200 here). I also want to know what exactly is meant by "powerful".
In general, there is no universal way to quantify the effect of a drug; the quantification procedure depends crucially on what effect the drug is supposed to have. For example, if the drug is supposed to decrease blood thickness, then a measure of the drug's efficacy is a measurement of change in blood thickness upon application of a given concentration of drug. So I'll focus on the case of analgesics, since that's the context of your original question.
While I can't say for sure how this particular quantity was measured, it appears that the effect of analgesics like morphine or enkephalins is measured by direct measurements of pain under different administered concentrations of drug. This can be done in animal or human studies. In animal studies, varying concentrations of a drug are administered, and then the response of the animal to different pain stimuli is recorded. One common example of a pain measurement is a hot plate, where the animal's foot is placed on a hot plate and the time until it tries to remove its foot is measured.
These studies can also be done in humans. In this study (1), the effect of a particular drug was measured by different tests, including
If these pain measurements are recorded when the patient has different levels of the drug in their system, then comparing drug effects amounts to identifying the concentration of drug at which a particular pain response is achieved. In other words
As a side note, the initial thought I had was that this might be measured by quantifying the receptor-ligand affinity of the various drugs for the pain receptors (opioid receptors) in the nervous system. In that situation, saying that drug A was 200 times more powerful than drug B would amount to saying that A's affinity (or Kd) for a particular receptor was 200 times greater than B. Or something along those lines (see the Wikipedia article on receptor-ligand interactions). That would be a 'universal' way to measure drug efficacies, since a large number of drugs work by blocking certain receptors in the brain. But biology is too complicated to permit a straightforward relationship between binding affinity and perceived drug effect. At least, not yet!
References and Further Reading
(3):Estrup Olesen A et al. (2012). Pharmacological Reviews 64(3):722-779 Extensive review of this subject.