In an Inferential Statistics test, a Beta Error is a "False Negative" (in contrast to an Alpha Error, which is a "False Positive"). Power is the Probability of not making a Beta Error. It is the Probability of correctly concluding that there is not a Statistically Significant difference, change, or effect. Put another way, Power is the Probability of accepting (Failing to Reject) the Null Hypothesis, when the Null Hypothesis is true.
Power is directly affected by Alpha, the Level of Significance, and n, the Sample Size. If we want to increase the Power of a test, the best way is to increase the Sample Size, n.
We could also increase Alpha. Alpha is the value we select as the maximum Probability of an Alpha Error which we will tolerate and still call the results "Statistically Significant". So, if we're willing to tolerate a higher Probability of an Alpha Error, we can reduce the Probability of a Beta Error. This is illustrated in my blog post on the Alpha Error and Beta Error see-saws.
As the two see-saws in the middle of the graphic above demonstrate, Power has an inverse relationship with Effect Size (ES). If we want our test to be able to detect small Effect Sizes, then we need to have a high value for Power. As we just said, we can get this by increasing the Sample Size, n, or increasing our tolerance for an Alpha Error.
The 2nd see-saw above shows that if we have low Power, then the detectable Effect Size will be high.
Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.