A friendshipdrink is usually used when some-one at a party does not want to have another alcoholic drink of some sorts.
When a friend wants to push this person who does not want to drink, he will say that this drink is a toast to their friendship.
This will usually make the person go "okay let's have one..." resulting in the person getting more drunk or even getting in the state of victoring.
This "technique" is widely used at private parties and clubs in Europe.
Jason: "Let's have another drink!"
Arnold: "Nah I've had anough"
Jason: "But this is a friendshipdrink, it represents our friendship!"
Arnold: "Okay ONE more and that's it"