Precision is the detail with which something is expressed. Accuracy is how true that expression is. “It’s 5:17” is more precise than “it’s quarter past five”. But if it’s actually 5:13, the second statement is more accurate.
The problem with precision arises because accuracy is often difficult or impossible to assess, but precision is easy to determine (e.g. quantitative answers are always more precise than qualitative ones). And humans have a cognitive bias to assume greater accuracy when present with greater precision.
This may have been a reasonable heuristic historically, when precision was also hard to come by. But with the rise of computing power generating arbitrary amounts of precision, without a shred of accuracy in sight, has become trivial.
This manufactured perception of accuracy extends beyond numbers and statistics, to include detailed models and simulations as well. And using this perceived, but fake, accuracy is a key source of the deception of the “expert” (although in fairness, most of them are fooling themselves as well).