What does “v” correction for Sun, Stars, Moon and Planets mean?

A number given in the Nautical Almanac that is used to correct the Greenwich hour angles (GHAs) of the moon and planets.This correction is not needed for the sun and stars because they circle the earth at precisely constant rates according to GMT.

The stars do this because they are stationary and the earth rotates at a constant rate (15° 02.5′ of longitude per hour). The sun also does so (at a slightly different constant rate, 15° of longitude per hour, exactly) despite its annual motion through the stars as we circle it, because GMT is defined in such a way as to make this happen. But because of the orbital motions of the moon and planets, their GHAs do not circle the earth at constant rates, but rather vary slightly throughout the month for the moon and throughout the year for the planets. 

The Nautical Almanac accounts for this variation by assigning each a constant average value (15° 00.0′ per hour for the planets and 14° 19.0′ per hour for the moon), and then lists the excess of this rate at a particular time as the v-value. For example, if the moon’s v-value is listed as 14.0′ at a GMT of 22h 00m, it means that at this time of day, the moon’s geographical position is moving west at a rate of 14° 19.0′ + 14.0′, or 14° 33.0′ of longitude per hour.

If you wanted the moon’s GHA at 22h 49m 10s,  you would look up the GHA at 22h on the daily pages and then find the 49m 10s increment on the 49-minute page of the Increments and Corrections Table. This answer should be (49m 10s) x (14° 19.0′) / (60m) = (49.167/60) x (14.317) = 11.732° = 11° 43.9′, which must be added to the 22h value.then find in the same table the v-correction that corresponds to a v-value of 14.0′. This should be (49.5m/60m) x (14.0′) = 11.6′. Add this v-correction and you have found the proper GHA. Note that the corrections table uses the half-minute value (49.5 instead of 49) for all times. 
The v-value and subsequent v-corrections are positive in all cases except occasionally for Venus, in which case it is clearly marked in the Nautical Almanac.