Ok, what it depends on is how many seconds it takes for the attacked unit to escape your range. Let's set everything to one for an example!
If your attack range is 700 and your tower (I'm assuming you want to know this for a TD), is "floating" above the path (not possible but I'm simplifying it), a unit with a speed of 1400 (1400 units per second) will be able to leave the tower's range in one second, meaning the tower gets to attack the unit for one second. Remember the attacking range is the radius and the target's "escape range" is the diameter. If the tower attacks once per second and deals one damage per second, it will be able to deal only one damage to one unit.
Now, a unit with a movespeed of 1400 is not likely at all unless you want your game to crash. Most units have a movement speed of 300. If your tower's range is a little over 600 and it's NOT floating, and it's on a flat edge that's not near any turns in the path or corners, then its range of attack (as far as the path is concerned) is 1200. If the tower attacks twice per second with a damage of 50 (100 dps), it will deal 400 damage to one unit.
Don't forget -- range actually doesn't change the damage per second, only the total damage it can deal to one unit. The total damage is the DPS multiplied by the number of seconds, rounded down to a multiple of the attack cooldown (because if it attacks once every 1.3 seconds, and you have 3 seconds to attack, it's really the same as having 2.6 seconds since you can't get the next attack at 3.9 seconds)
Range is a major factor in determining total damage dealing capability, but only in theory. In my example, there is only one unit being attacked. In a real TD, some towers have splash damage; others have slowing attacks. Also large waves of creeps will come so the tower cannot attack every creep that comes into its range unless it has a multiple-strike power like in Green TD.
The terrain also changes the effective range of a unit or tower. A tower has more effective range if it's placed on a roundabout or a corner, for example, than if it is placed on a flat side or next to the unit spawn point (which usually makes the units invulnerable while standing there).
