Pi (π)
Draw a circle with a radius of 1 The distance half way around the circle is 3.14159265... 
Or draw a circle with a diameter (all the way across the circle) of 1 Then the circumference (all the way around the circle) is Pi 
So Pi (the symbol is the Greek letter π) is: The ratio of the Circumference 
To help you remember what it means
just draw this diagram.
Finding Pi Yourself
Draw a circle, or use something circular like a plate.
Measure around the edge (the circumference):
I got 82 cm
Measure across the circle (the diameter):
I got 26 cm
Divide:
82 cm / 26 cm = 3.1538...
That is pretty close to π. Maybe if I measured more accurately?
Digits
In fact π is approximately equal to:
3.14159265358979323846…
The digits go on and on with no pattern. π has been calculated to over two quadrillion decimal places and still there is no pattern to the digits
Example: You walk around a circle which has a diameter of 100 m, how far have you walked?
Distance walked  = Circumference 

= π × 100 m  
= 314.159... m  
= 314 m (to the nearest m) 
Approximation
A quick and easy approximation for π is 22/7
22/7 = 3.1428571...
But as you can see, 22/7 is not exactly right. In fact π is not equal to the ratio of any two numbers, which makes it an irrational number.
A better approximation (but still not exact) is:
355/113 = 3.1415929...
(think "113355", then divide the "355" by the "113")
Remembering The Digits
I usually just remember "3.14159", but you can also count the letters of:
"May I have a large container of butter today"
3 1 4 1 5 9 2 6 5
To 100 Decimal Places
Here is π with the first 100 decimal places:
3.14159265358979323846264338327950288 4197169399375105820974944592307816 4062862089986280348253421170679... 
Calculating Pi Yourself
There are many special methods used to calculate π and here is one you can try yourself: it is called the Nilakantha series (after an Indian mathematician who lived in the years 1444–1544).
It goes on for ever and has this pattern:
3 + \frac{4}{2×3×4} − \frac{4}{4×5×6} + \frac{4}{6×7×8} − \frac{4}{8×9×10} + ...
(Notice the + and − pattern, and also the pattern of numbers below the lines.)
It gives these results:
Term  Result (to 12 decimals) 

1  3 
2  3.166666666667 
3  3.133333333333 
4  3.145238095238 
...  ... etc! ... 
Get a calculator (or use a spreadsheet) and see if you can get better results.
Pi Day
Pi Day is celebrated on March 14. March is the 3rd month, so it looks like 3/14