The more digits of pi you use, the more accurate your calculation. For example, using 3.14 is more accurate than using a value of 3. The value of pi has been calculated to trillions of digits (the record at the time of this post is a little over 10 trillion digits). However, the push for more and more digits of pi has more to do with a desire to break records and test computer algorithms than any need to be more accurate. It would never be necessary to use more than a few digits of pi. In fact, you only need 39 digits of pi to calculate the circumference of the known universe to an accuracy that is within the width of a single hydrogen atom.
Pi rounded to 39 digits: 3.14159265358979323846264338327950288420
Numberphile explains the calculation in his video: