The 3 eyes refer to the 2 "actual" eyes and the penis eye- where spunk comes out. This cleverly ties in with the fact that all 3 eyes produce a fluid- whether it be tears or spunk.
It usually takes place when a man is upset and proceeds to cry.. but comforts himself with a wank (whilst still crying obvs)
John 2: "Whadup bro?"
John 1: "I just fell off my BMX and got a splinter in my pinkie"
John 2: "Hahah chode!"
John 1: "Im off for a 3 eyed cry. Sob"