It's definition is a little hard to understand, but it is the distance where 1 Astronomical Unit (AU) subtends an angle of 1 arcsecond (or #1/3600# of a degree). It is equal to 3.26156 light-years.

See the picture below for a visual.

Let's do the calculations. Let #R# be the distance of a star 1 parsec away and #r=1AU# be the radius of the Earth's orbit and #theta# be the parallax angle which is 1 arc second by definition. As the angle is small we can use the formula #r=R theta#, where #theta# is in radians to relate the values.

Converting #theta# to radians gives:

#theta = 1/(360*60*60) * pi/180#

So, we can calculate the value of a parsec #R# in AU as:

#R=r/theta=1/theta=(360*60*60*180)/pi=206,264.8AU#

Now #1UA=1.58125*10^(-5)# light years.

We ccan now calculate the value of a parsec in light years as:

#R=206,264.8*1.58125*10^(-5)=3.26156# light years.