Pearls are a special collectible resource introduced to the game in the Shifters expansion. They are used to unlock Blessings at the Altar of Auriga, build blessing-related improvements, and influence future Winter Effects.
When Winter arrives, pearl clusters will appear at random locations across the map, with a tendency to appear more frequently on Anomalies. When a unit moves over the tile containing the cluster, a variable amount of pearls will be added to the faction's collection, tallied above the 'End Turn' button in the bottom-right controls interface. In general, it is advised to have units with the Auriga Affinity capacity collect pearls, since it will increase the amount collected from each cluster slightly. Allayi Heroes and Skyfins have Auriga Affinity 1 and 2 respectively, granting +10% and +20% pearls collected from each cluster, but it is possible to equip heroes with the Eyes of Auriga accessory after unlocking the Pearl Crafting blessing, which will give the equipped hero Auriga Affinity 3, increasing the yield of pearl clusters by 30%.
Pearl clusters will remain on the map until they are collected, and the amount of pearls in a cluster may increase with subsequent winters if the cluster isn't collected. Note that building a district over a tile with a pearl cluster on it will destroy the pearls, and clusters will no longer spawn on that tile.
From the strategic map (zoomed out), you can see where pearls are located by an icon of a white ring, with a number of small white dots to the top-right of the ring indicating how many pearls are in the cluster; 1 dot means only 1 or 2 pearls, while 4 dots means 10 or more. You can also see exactly how many pearls are in a cluster by hovering the mouse over the tile the cluster is on.
Pearls can also be acquired through trade with other factions, although the AI is generally very reluctant to give them away.
As mentioned before, one of the main uses of Pearls is to unlock Blessings, and then make use of the things those blessings unlock. Blessings become available to unlock after having built the Altar of Auriga in one of your cities, and then each tier is unlocked by subsequent winters; the inner ring unlocked at the start of the first winter, the middle ring unlocked at the start of the second, and the outer ring unlocked at the start of the third. Because of this system and the fact that the Altar of Auriga requires pearls to be built in the first place, the Allayi are the only ones who can build the Altar before the first winter, since they're the only ones that can collect pearls through searching ruins.
Each tier of blessings requires more pearls to unlock, and then the things they unlock require pearls to be built as well. These blessings range in usefulness, and some are very situational, but some can be very beneficial - such as the Winter Borough. A full breakdown of all the blessings and what they unlock can be found on the Blessings page.
The other main use of Pearls is to vote for the new effect that will become active on the next winter. Again, the Altar of Auriga must be built to access this feature, but after the first winter is over, a list of three potential new effects to be added in the next winter will be present on the Altar of Auriga screen, with the number of votes cast for that effect to their right. You can spend pearls to vote for a particular effect over the others, which grants you some degree of control over how winters progress, allowing you to potentially rig winters to your favor - for example, a Broken Lords empire may vote for effects that reduce the amount of Food cities produce, since that won't affect them at all, but will be a detriment to their enemies, giving them the upper hand.
However, voting for winter effects can be very costly, and may not be a viable strategy for empires with limited access to pearls. The cost to cast a vote is equal to the number past winters plus the number of turns that have passed since the previous winter; for example, if three turns have passed since the end of the first winter, the cost to vote on a winter effect is 4 . Without access to a large amount of pearls, it can often be more beneficial for empires to prioritize unlocking and making use of blessings over voting for winter effects.