Looks like maybe a small opamp driven MOSFET design that regulates on the negative side (meaning it can't be common grounded). If so, it wouldn't be a boost driver, but rather it would need the output voltage (to the LD) to be lower than the input. By how much? I'm not sure. It's probably a design that was used for green modules, possibly adapted to run higher output voltages, or just straight from one of the "module" type of green lasers. Greenies don't need a "boost" circuit since the IR diode is usually around 2V or so, meaning a 3V source can be enough to run one of these drivers for it, but it certainly wouldn't be the same for say a red or a violet diode. It also looks like part of the pot creates a series resistance between the positive input and output, so you definitely want to make sure your LD positive and negative are isolated from the LD case or that your LD case (and heatsink) are isolated from either battery pole.
And, the TTL is just so that you can modulate the output, but it looks like it's rated to a pretty low frequency, so it wouldn't really be useful for lasershow type of applications. I'm not really sure how it works... TTL grounded being the off trigger, a modulated input voltage or something else?
Also, it has the two pads being "LD ' - ' or null" and "LD ' - '", however those pads are not common, and one is probably designed to be a feedback to the driver from a photodiode.... not sure how that works, then.