I've found two different meanings of precision:
Meaning 1 (from Grade 11 Physics textbook,India):
Precision tells us to what resolution or limit a quantity is measured.
Meaning 2 (from Grade 11 Chemistry Textbook,India):
Precision refers to the closeness of various measurements for the same quantity.
It's really confusing to have two different meanings for the same term. I think, textbooks can't be wrong. Does this mean that precision in physics is different from precision in chemistry?
Not at all. Those definitions of precision do not have opposite meanings, just different. The first one refers to the number of digits a given measured quantity can have (its resolution). For example, the speed of light in vacuum is measured to be:
$$ c = 299\,792\,458 \rm\, m/s $$
Which is precise to the 9th digit. Other experimentally measured quantities may have different precisions like the mass of the electron, which precision or resolution offers 2 more digits.
$$ m_{e} = 9.109\,383\,7015 \times 10^{-31}\rm\, kg $$
The second meaning you've found is related to a different aspect of precision. If you perform an experiment whose outcome is one quantity, you may perform it again and again some number of times $n$. If each result from each experiment is close together with the remaining ones, then the overall result is said to be precise. If they are not, meaning that they are spread out, then the overall result is imprecise.
The first definition refers to the precision of a single measurement, whereas the second refers to the precision of a group of measurements.
Suppose I have a digital stopwatch that measures time in seconds with three decimal places. If I make one measurement of the period of a pendulum I will get a value that has a precision of one thousandth of a second. If I make ten measurements of the period of the same pendulum then those measurements could be spread over a range of one tenth of a second or more - the limiting factor is now my reaction time, not the precision of the stopwatch. Note that we have said nothing so far about the accuracy of the measurements - if the stopwatch is faulty then they may be precise but very inaccurate.
Accuracy is the degree of closeness of readings to the value relative to an agreed standard.
Precision is the closeness of the measurements to each other.
I like this sort of image when differentiating between precision and accuracy.
The true value is the centre of the target.
A 101 cm long rule with calibration marks indicating that it is one metre long will produce readings of length with approximately the same precision as a metre rule which is one metre long as compared to the SI definition as the metre, but will not be as accurate.
The inaccurate rule will measure an accurately measured length of 100 cm as 99 cm.
