The "Hand Mounted Repulsor", or "Manual Hand Repulsor" is a emergency weapon created by Tony Stark to allow him to use his repulsors while not using the armor.
The "Hand Mounted Repulsors" look like the shape of the repulsors in the Iron Man Armor. It is just the circular shaped repulsor part of the Iron Man Armor attached to Tony Stark's "Vibranium Core Arc Reactor Mark II". After it's use, the Repulsor withers away, making it a single-use weapon.
After the events of the "Avengers", Tony Stark created the "Hand Mounted Repulsor" to allow him to use his repulsors while not using the armor. Later, the weapon was used by Tony to blast Eric Savin after Harley Keener distracted him with a flashbang from the Mark 42. Unfortunately, while the repulsor knocked Savin out for awhile, he survived due to Extremis. The repulsor also withered away after one use.