2 a: the degree of refinement with which an operation is performed or a measurement stated — compare accuracy 2b
So why are they important for product managers?
If you are accurate without being precise, there is a good chance that your work output is of adequate quality. However, it may contain unpredictable variance. In target practice, this is similar to hitting the outer circle consistently while never hitting the bull’s eye. Which means, that while 100% of the product use cases are okay, none of them are capturing the exact user requirements. This can be a distraction to the engineering team and increases the risk of faulty product development.
On the other hand, if you are precise without being accurate, you can have 100% of use cases correctly defined and excellent in describing the user needs. However, you can be very wrong about the intended user. (It is like shooting at the wrong target.) This will guarantee that the software release bombs or does not meet the target parameters.
Accuracy with Precision
A good product manager is both accurate and precise. The accuracy comes from knowledge of customer and market needs and the precision comes from the skills learnt either in the classroom or on the job. Only when you have both can you create awesome requirements, which are translated into wonderful products.