What is the structural difference between 3 ATM, 5 ATM and 10 ATM watches?

The level of sealing, of course. A 3ATM watch is equivalent to about 30m of water pressure, but contrary to popular belief DOES NOT mean you can submerge the watch. They are splashproof and rainproof but should not be worn in the shower.

A 5ATM or 50M rated watch can be worn in the swimming pool, and usually features one or more sealing O-rings under the case cover and in the bezel and adjustment dials to keep water out.

a 10ATM watch is where most reasonably priced watches for snorkelling and watersports like surfing come in. Manufacturing tolerances are tighter, seals are better, enduring even heavy usage submerged in water.

Above that, the 20ATM is the first watch capable of actually skin diving (no scuba tanks) and the structural differences start to vary greatly. I have a 30ATM watch and whilst it's great because I can scuba dive with it on, its really not great when the battery runs out; The costs for servicing/testing are enormous.

Structurally, they are very precise and well sealed (often the crown wheels screw down into place and seal also) but critically, they have a gas reserve inside the watch. This compensates for pressure inside the watch so that when you ascend from a deep dive, the crystal watch face doesn't burst out of the bezel.