This is the range in map squares at which the attack can be performed. 0 means only on your own square, 1 includes any adjacent square, 2 any square adjacent to those, etc.
Range is mainly determined by the type of weapon used. Daggers and knives have a range of 0, longer melee weapon a maximum range of 1 or sometimes 2. Slings and bows range even further, however, these cannot be used for attacks on your own location and have a minimum range of 1.