Both Uthid and Vanasha are characters that are first introduced in Horizon Zero Dawn. By the time that Aloy meets the two, Vanasha is deep undercover and Uthid is being hunted for crimes he didn't commit. All this has to do with the politics involving the Carja and the Shadow Carja.
Who is Vanasha
Vanasha is Marad's best agent, a spy as good, or even better than he is. Suffering from abuse from many of the Shadow Carja's nobles, she became hateful of them. Her training as a Carja spy made her infiltration of the Shadow Carja easy and she would become a direct handmaiden to the Queen, Nasadi. After seeing how Nasadi and Itamen were held as prisoners rather than as royalty, she revealed herself to them and convinced them to defect to the Carja.
By the time that she meets Aloy, Uthid is being accused of attempting to kill the Sun-King, Itamen. Vanasha's desire to protect Uthid and enlist Aloy's help came from her spending so much time with Uthid, Nasadi, and Itamen and seeing that they share the same ideals. Making both Itamen and Nasadi defect to the Carja and anointing Avad as the Sun-King makes the Shadow Carja fall apart. Aloy's help in saving Uthid, killing his accusers, and helping Nasadi and Itamen couldn't have happened without all the work that Vanasha put in for two years as a spy.
Who is Uthid?
Uthid was a Carja soldier who then became part of the Shadow Carja after Helis and Bahavas established the group. He joined them as a means of following Itamen, who he believed was the true Sun-King rather than Avad. Avad and Itamen were both the sons of the previous Sun-King, Jiran, of whom Uthid served loyally. Because Helis and Bahavas used Itamen as a figurehead, they gained a lot of power as a separate faction, the Shadow Carja.
Eventually, Uthid started having doubts about how Helis and Bahavas were running things and in response, Bahavas tried to kill Itamen. Uthid stopped this attempted murder, turning in the assassin to Bahavas himself not knowing he was the one that ordered the hit. In response, Uthid was then hunted by Bahavas's men to cover up his evil plans. Vanasha recruited Aloy to help save Uthid and clear his name, killing the groups of bounty hunters that were after him. After being saved, Uthid defected back to the Carja until his name was cleared and became the military advisor to Avad. Both he and Vanasha fight alongside Aloy in The Battle for Meridian.
For more Horizon: Forbidden West guides, check out What is Project Zero Dawn in Horizon Forbidden West? on Pro Game Guides.