What is current modulated laser driver? What does it do to the laser?
The resistance of a semiconductor laser is low and strongly related to temperature and too much current flowing can easily damage the laser. 

The electronics driving the laser controls (adjusts) the voltage such that the desired current flows through the laser by measuring the voltage across a sensing resistor. This is a constant current source. 

If the optical output of the laser is to be modulated - its amplitude is changed with time - this is accomplished by changing the voltage supplying the laser (and measuring the current flowing through the laser) then the device driving the laser is called a current modulated laser driver.  The driver can only work so fast - this is the bandwidth of the modulation.

You would likely drive the input to the electronics module with a modulating voltage that varies between off  (actually a voltage that corresponds to a current which is just about the lasing threshold) and the maximum desired optical output. You'll need a device that can do this at the rate you require - some sort of pulse generator.

Because the driver has a finite bandwidth the rise/fall times of the optical output will be limited. (Higher bandwidth sharper edges).

You'll need another controller to measure and control the temperature of the D2570 - \$\lambda\$ is sensitive to laser temperature. The D2570 has a pins for an on-board TEC and pins for a thermistor to monitor the temperature.

Connecting a laser to a constant voltage supply with croc clips is a bad idea.