Power is the probability of a statistical test to detect a meaningful effect.
Just as a sample of your blood indicates what's going on in your entire bloodstream, when we draw a sample we try to make some valid inferences about the population by observing a portion. An important mathematical concept, the Central Limit Theorem, states that as sample size gets bigger it more closely approaches a normal distribution. What this means is that larger samples are better estimators of population effects than smaller samples. Sampling error refers to the understanding that the sample we select is not exactly the same as the population, no matter how large the sample. If we were to take repeated samples from the same population, the sample statistics would vary a little from sample to sample.