The Remnant are a group of people in Rise of the Tomb Raider. They are the descendants of the citizens of Kitezh that were forced to live in the wilderness of Siberia after the city was lost to them during an Mongolian invasion.
Lara discovers them in Siberia and soon allies herself with them as they are also threatened by Trinity. The first time Lara hears about the Remnants is in a Cut Scene in the Siberian Wilderness while listening to Trinity radio chatter at the Wilderness Refuge Base Camp:
She later discovers them in person when she is threatened by Sofia to abandon her search, but she soon is able to gain their trust by helping them out on multiple occasions.
They provide Lara with side quest missions that reward her with special items like e.g. the Lock Pick and open up access to certain areas that previously were unavailable to her. All missions presented to Lara by the Remnants are optional. The main story of the game can be played without these side quests.
Later in the game Lara fights side by side with them against Trinity soldiers and the Deathless that now occupy the lost city. In the end Lara is well respected among the inhabitants of the valley.
History of the Remnant
The Forefathers: Byzantine Empire
The Apostle set of documents gives an account of the live of the forefathers. The Prophet seems to have come to Constantinople around 970 AD and soon gathered a lot of followers. At first they were left alone, but soon the "Church in the West" began to take notice and sent the Knights of the Order of Trinity to put an end to the heretic teachings of the Prophet. The left the Byzantine Empire around 977 AD for Syria.
The Forefathers: Exodus
Trinity followed the forefathers to Syria and the Prophet was slain. His people build a tomb for him but to everyone's surprise he came back to life, rallied his supporters, and fought of the Trinity knights. As they no longer were save in Syria they decided to leave the Empire for good, turning north towards Sibera.
They sent ahead a group of workers to prepare for the arrival of their people. These workers made sure that everything necessary to make this new place their home was provided, like a supply of fresh water for which purpose they created the Ancient Cistern.
The Forefathers: Kitezh
Life in Kitezh was good and the city grew. There were baths, churches, a hospital for the sick.
When the Soviets came, they took the Remnant they encountered hostage and made them work the mines. When their forefathers history was uncovered by their oppressors however the Remnant rose up and rebelled. 
- ↑ Correspondence from the Ancient Cistern set of documents.
- ↑ Document Resistance