Who was Chur?
Rashi: He was the son of Miriam and Kalev.
Why was it necessary for Aharon and Chur to accompany Moshe up on to the hill?
Rashi: They were fasting; 1 and we learn from here that on a fast-day, three people must stand by the Amud. 2
Chizkuni: The Torah needs to mention them, so that, when it writes (in 17:12 below) that "they took a stone ... ", we know who "they" is referring to.
QUESTIONS ON RASHI
Rashi writes: "Chur was the son of Miriam." Why is this significant?
Gur Aryeh: Why didn't Moshe select Aharon's sons Nadav or Avihu, to accompany himself and Aharon in leading the Tefilah? Rather, Moshe chose Chur because he was the son of Miriam - so that all three of the leaders of Am Yisrael would be represented, and in their merit they would overcome the enemy. 1
Maharal (Netzach Yisrael Ch. 54, p. 200): Michah 6:4 tells us that Moshe, Aharon, and Miriam all were Hashem's messengers in taking Yisrael out of Mitzrayim. Aharon's role was to pursue peace, bringing together and unifying Yisrael as a nation; later he became Kohen Gadol, fostering their connection with Hashem. Moshe was the leader (and in effect king) - defining Am Yisrael's direction and making them one. Miriam represented Yisrael's yearning (which is feminine in concept) for Hashem and His redemption. Gur Aryeh is telling us here that all three of these traits were needed in order to counter Amalek. Maharal concludes (Netzach Yisrael, ibid.) that at the future Geulah, there will be only two redeemers - Eliyahu ha'Navi, filling Aharon's role in bringing peace; and the Melech ha'Mashiach in the role of Moshe, as leader. We will not need, however, a third leader to help us yearn for and return to Hashem - rather, it will be inherent within us.