SH3 is one of those games that you need to invest time in. It is a perfect example of a "Dad game," as Yahtzee Crowshaw once put it. It's meticulously detailed, and you must learn all of the different eccentricities of the sub to be a great captain.
It uses the real-life technological limitations from WWII to define the gameplay. Want to fire off a torpedo? A standard gas-powered torpedo leaves a trail of bubbles in the water, which ships can detect in advance and will swerve to avoid your torpedo. You can fire an electric torpedo, but you'll need to be close, or else the battery in the torpedo will die and it won't reach your target. SH3 is filled with these sorts of tactical nuances that really make it satisfying to play.
Difficulty is customizable. It can be as simple as "point the periscope at a target and shoot," to manually identifying and anaylizing your target's position relative to your own. Difficulty is increased by making the game more akin to real life (limited air, limited fuel, no periscope stablilization, etc.) This helps tremendously, since beginners can relax the difficulty while they familiarize themselves with the ships' systems.
The player is awarded more renown following a mission with high difficulty, compared to a mission with a lower difficulty setting. Renown is SH3's version of experience points. It allows you to 'purchase' upgrades for your sub like improved batteries, hydrophones, conning towers, or even a completely different sub altogether. Medals are awarded after each mission, which you can assign to your crew. This is probably the single most satisfying part of the game; the medals allow your crew to function more efficiently, thus improving things like torpedo reload times.
There's a lot to cover here, so let me just wrap this this up by saying that this is probably the best simulation game I've ever played. I find myself coming back to it every couple of weeks. It's aged quite horribly, but I don't care, since the gameplay is just too good. Forget the sequels in this series, SH3 is the best.