What kind of unit was this?

[panzerschreck1]

V°-Meßtrupp 506

Can anyone explain what this unit specifically did?

[Leo Niehorster]

V° is the designation for muzzle velocity. These artillery calibration units belonged to the artillery arm, and measured the muzzle velocity of artillery weapons.

The reason for V° units is indicated by the modern day US Army field manual:
To obtain accurate artillery fire, the performance of the weapon projectile family-propellant type-charge combination must be known. If it is not known, the result can be reduced effects on the target or friendly casualties (for example, danger close, final protective fire [FPF], converged sheafs, and so on). Firing tables give standard muzzle velocities for a standard weapon firing standard ammunition under standard conditions. However, muzzle velocities achieved in actual firing may differ from the standard muzzle velocities because of variations in the manufacture of the weapon and ammunition, wear in the weapon tube, projectile weight, propellant temperature, propellant lot efficiency, or a combination of these factors.
FM 6-40, "Field Artillery Manual Cannon Gunnery", Department of the Army, Washington, DC, 23 April 1996
[Thank you Google]

They existed as independent light units (ca. 10 men), and as independent heavy units (ca. 25 men, containing a small headquarters detachment and two of the light units).

Cheers
Leo

Correction:
Sorry - checked my sources at home - there were no V°-Meßtrupps in the artillery observation batteries or battalions. Hence, this phrase has been deleted from above statement.

[panzerschreck1]

Thanks Leo, good info!