Precision is how fine a measurement is (i.e. being able to measure temperature to thousandths of degrees versus tenths), whereas accuracy is a measure of how closely your results much the objective truth. So you may have a very precise thermometer that measures to thousandths of degrees but it may not be accurate because it's calibrated such that it always reads exactly two degrees higher than it should. Meanwhile a thermometer that can only measure to a tenth of a degree is more accurate and less precise than the one just mentioned if the shown figures reflect the true temperature.

In common usage, these words mean the same thing, but scientists often give words specific meanings in order to make their research and ideas less ambiguous.

Definitions are even more important in non-scientific fields such as philosophy or math where meaningful reasoning of abstract structures and ideas would be next to impossible without giving them concrete definitions and stating your assumptions.

Remember that definitions are arbitrary, so to understand an author's argument or idea, you must seek out the author's definitions.

Hopefully that clarifies some of the discussion going on in the comments here.