March 14 (3/14) is celebrated annually as Pi Day because the date resembles the ratio of a circle’s circumference to its diameter — 3.14159265359... or, rounded off, 3.1416. 2016, therefore, provided a particularly good reason to celebrate: 3/14/16. The year before (3.14.15) was significant because it matched the first four digits after the decimal point - now we're back to regular old Pi.
Archimedes (wiki) (circa 287–212 B.C.) is credited with doing the first calculation of Pi. British mathematician William Jones came up with the Greek letter and symbol for the figure in 1706, the use of which was later popularized by mathematician Leonhard Euler (wiki), beginning in 1737.
Here's Vi Hart on 2016 Pi Day:
And a good general explanation of Pi (kid-oriented, but that makes it straightforward):
And here's what Pi sounds like: