In simple words, what is the prediction accuracy? What is it based on? How does it help? When is it used?
The accuracy of a model is defined as the number of correct predictions divided by the total number of predictions. The expression "prediction accuracy" refers to the accuracy of the model at doing predictions.
For example, suppose that you observe the sequence of numbers $1, 1, 2, 3$. What would be a likely next number of this sequence? The operation of guessing this number is called a prediction. These are numbers of a Fibonacci sequence, so a model could predict $5$ as the next number of this sequence. However, it could also predict e.g. $2$ because the complete sequence could be $1, 1, 2, 3, 2, 1, 1$. Which prediction is correct? It depends on the problem. Do we want the model to predict the numbers of the Fibonacci sequence or of another sequence? Suppose that we want the model to learn the Fibonacci sequence and the models predicts another number different than $5$, then this will be considered an incorrect prediction.
A model that produces incorrect predictions is useless. So, we want models that have high accuracy. However, accuracy is not always the best measure of a model's performance. See e.g. Why is accuracy not the best measure for assessing classification models?.
There are several related terms and concepts, such as inference, forecasting or deduction. They are sometimes used interchangeably, even though they might have slightly different meanings or definitions.