When you read a statement like, "Did you know that 42.73% of all quoted statistics are just plucked from the air?", you should be able to see the difference between accuracy and precision immediately. The statement is very precise since 0.01% means one part in 10,000 but you know it can't be accurate because of the impossibility of measuring something like that. Too many people use the words interchangeably, so if you're one of them stop doing that!
Anytime we measure something, we can only do it with a certain degree of accuracy depending on the equipment we use and the conditions under which we work. If we know the accuracy of our equipment and the effect of the conditions under which we work then that should tell us how precisely we should state the answer. If you're using a ruler whose smallest divisions are 0.1 inch and the item you're measuring falls between two of the divisions, you might estimate the 0.0x or hundredths digit to be a 3 say but you should indicate this by recording your measurement as xx.x3 plus or minus say 0.02 or 0.01 indicating that you were guessing the last digit and also how accurately you thought you could geuss it. The 0.01 or 0.02 is sometimes called the "precision" of the measurement. In science, more accurate measurements often tell us that our theories and laws need to be changed and the precision of our measurements tell us how sure we are that they need changeing.