In Destiny, Strange Coins are a form of currency that you can use to trade with Xûr, Agent of the Nine when he is in the Tower.
Xûr only shows up in the Tower on the weekends, from early Friday morning (9am GMT) to early Sunday morning (also 9am GMT.)
You’ll have to save your Strange Coins during the week and visit him in the weekend in order to purchase the Exotic loot he has for sale. His available items for purchase are different every week as well.
You can acquire Strange Coins in multiple ways.
One of the most reliable ways to get Strange Coins is to make sure you complete the Weekly Heroic Strike mission every week. These grant 3 coins at level 24, 6 coins at level 28, or 9 coins at level 30.
You can’t get more than 9 Strange Coins this way per week (per character), since doing a higher difficulty Heroic Strike will only give you the difference between what you’ve already gained vs. what is granted by that difficulty.
The most efficient way to farm Strange Coins is to have three high level characters that can run the Weekly Heroic Strike at level 30 difficulty once per week. Doing this will give you a minimum of 27 Strange Coins per week.
If you have capped out your Strange Coins for the week from the Weekly Heroic Strike, the following will also grant you Strange Coins randomly: