Its a Darlington pair so is two transistors integrated in a single package - see fig 2 on datasheet page 2. The 2.5V Vbe is worst case when passing 3A. See the left hand fig. 10 graph, line Vbe(sat) @ Ic/Ib = 250, which indicates that for Ic=2A and Ib=8mA (by definition from the ratio), you can expect Vbe to be about 1.7V. At 8mA output current the Arduino output will be a bit above 4.7V (see fig. 33-24 in the full ATmega328P datasheet), so the base resistor will be dropping about 3V while passing 8mA, which gives 375 ohms. 330 ohms is the next lower E12 preferred value, which will give a bit under 10mA Ib, plenty for saturation with a 2A load, and not too much for the Arduino I/O pin (unless you have too many pins driving the same type of circuit).
However Fig. 10 also shows you that the Vce(sat) @ 2A will be about 1V, (a penalty of using a Darlington) so with a 12V supply your load will only get 11V. Also the transistor will be dissipating 2W, so will need heatsinking. If you need to drop less voltage or want to avoid the need for a heatsink, you'll need to use a N-MOSFET, and to make sure it turns on properly, select one with a Vgs threshold <2.5V.