Your Alliance consists of players on your Friends list and anybody you've played with recently. Each week, the XP they earn by playing Anthem can generate Coin for you through the Alliance System.
As your Alliance plays during the week, the XP they've earned counts towards your Alliance Tier. At the end of the week, that Tier pays out in Coin that you can use to unlock appearance options or other special offers in the store.
Only your top five contributors count towards your Tier. Friends get bonuses to their contributions, which are larger if you've played a mission with them.