Stop. You are mixing apples, and oranges, and bananas. Great fruit salad or dessert, but not good for comparison.
The Vf is the voltage required to get the rated current through the LED. Remember that Ohm's Law applies. It's a law like Gravity is a Law, it almost always applies (certain limited exceptions excluded, your mileage may vary, objects in mirror are closer than they appear, don't forget to take out the trash).
You can connect things electrically in series or in parallel. Voltage and current are distributed differently in series and parallel circuits.
As an example, make a stack of 3 NiMH cells. The voltage of each cell is nominally 1.2 V (hot off the charger they may be around 1.4 V each), so if you stack the cells head-to-tail you now have 3.6 V available from the pack. You made a series stack of the cells, so you add the voltage of each cell to get the total voltage the stack can supply.
What about the current, you ask? Whatever 'load' is put on the stack, is the current that is going through each and every one of the cells. So if the load is 750 ma, then 750 ma is going through each cell in the stack.
But my cells are 2500 mah cells, you ask? That is not the current of the cells, but the millamp-hour rating of the cells. It is how many millamps for how long that the current can be supplied. Think of it as how big the gas tank is on a car, a bigger gas tank has more 'juice' and can run longer than a smaller tank.
If you wired the cells in parallel, you would have 1.2 V from the pack but your amp draw from each cell would be 1/3 of the total amp draw.
What happens when I use a driver board, you ask? The driver board takes power in and sends power out, minus some losses. Electrical power is volts x amps = watts. But the driver may change the relationship between the volts and amps from the source to the load. An example mentoined is the Fatman, a boost circuit. It takes lower voltage and higher current from the cell(s), and sends higher voltage and a lower (controlled, incidentially) current to the load (LEDs for us, usually). It might take in 1.5 volts and 2 amps from the power supply, and send 3.6 volts and 750 ma to the LED (these are example numbers only, but the relative values are close to real-world). Notice that 3 watts of power went into the driver board, but only 2.7 watts came out? The board used up 0.3 watts internally (in this example), because nothing is 100% efficient.
Now lets look at the load side of things. Wire up three TWOH LEDs in series, and you would need to supply them with a total voltage of 3 x 3.03-3.27 V or 9.09-9.81 volts total for the spec current of 750 ma. If you wired them in parallel, you'd need to supply them with 3.03-3.27 V but 2.25 amps (watch out here with a driver circuit because the current limit from the driver board may be over what any one LED can withstand by itself).
One LED direct drive off of 3xNiMH cells? Like IssacHayes said above, use the TWOK. Watch out for fresh off the charger cells, they could be at about 4.2 V total. Way overdriven, maybe magic smoke range unless a big enough resistor is in the circuit to drop things down a bit [around 1 or 2 ohms, depending on how daring you want to be].
Tri-mag with a driver board? Pick your prefered tint and decide how much you want tint versus a little more efficiency from a lower Vf.
