Phi is a proportion or ratio - approximately
1 : 1.618
First defined by Euclid around 300 B.C.

Phi is the one and only point on the line where...
the ratio of AC to CB is the same ratio as
AB (the whole) to AC
phi =
1 : 1.6180339887499.....

Phi rectangles built within other phi rectangles to infinity, forms a golden helix
Phi can be derived in many ways.
Mathematically - try the square root of five PLUS 1 then divide by 2
It can be found in many relationships throughout the universe:
The Milky Way Universe itself 
The Human Face
The Last Supper
The Main Street Station Market Hall Layout!
The Nautilus Shell
DNA
Fractals
The path subatomic particles take when smashed together! 
Our Collective Consciousness?
. . .
When faced with a problem
where the solution is not obvious,
we search for the phi result.
-The People of Main Street Station - Public Market