(This post assumes a certain amount of knowledge about math.)
I think it's really cheesy to do something on June 28 just because the decimal expansion of τ begins “6.28...”, but well, I might as well do it today as any day.
If you've studied mathematics in the modern world, you've probably run into a number called pi, or π, which represents the ratio of a circle's circumference to its diameter. That's weird and confusing, because pretty much every other mathematical concept about circles is based on the radius of the circle, not its diameter. The diameter is exactly twice the radius, so lots of formulas involving π end up referring to the quantity 2π.
This is pretty silly, becuase the “2” in “2π” doesn't really mean anything. It's just a correction factor to make up for the fact that the number we're calling “π” is exactly half of what the natural value for the circle constant is. That leads to confusing things like the fact that rotating by π radians is a half-rotation, not a full rotation... and if you want to rotate by three-quarters of a circle, you have to rotate by 3π/2, which is completely confusing.
So, a lot of mathematicians, including myself, are now using a new name for the quantity “2π” – namely, tau, or τ. Its value is approximately 6.283185307..., hence the cheesy date of June (the sixth month) 28.
More information at http://tauday.com/.