I'm a bit of a skeptic when people tell me they can improve by solving tactic puzzles. Even though so many people believe it could... i'm just never convinced by it. Did Fischer improved by solving tacics? Did Carlsen? There are no written documentation anywhere that stated they became good from solving puzzles. I know most professionals will say they did a little of both and playing through GM games... but really, what if it's just an innate ability that wasn't honed by solving puzzles?
At start with puzzles you learn how the different tactics work. A true beginner recognizes a Pin or a Discovery but doesn't spot a Deflection or an Interference for example
The tactics help me alot to see little attacks. What is most difficult for me is to take it one step before that: how to set them up? Thats quite easy for simple discovered attacks, but most other tactics seem to happen suddenly without me setting them up.