Here's a simple, postage stamp description of what '4WD' is...
Part-time 4WD
Rear-wheel drive only for dry, paved surfaces while the driver manually selects 4WD via electronic activation (a switch on the dash), or by the transfer lever on the floor. When 4WD is engaged, the transfer case locks in so power is split equally between front and rear wheel sets.
Advantages: Simplicity and less wear and tear on mechanical components, and slightly lower fuel consumption in 2WD mode.
Disadvantages: 4WD can be used only on slippery surfaces (such as dirt or gravel roads, or very wet paved roads) or transfer case damage can occur.
Full-time 4WD
Keeps all four wheels at the ready to receive power at all times. In extreme conditions you can be stuck with one wheel spinning, so most have other traction aids, from a simple locking centre diff (which makes the system effectively part-time), to electronic traction control.
Advantages: Gives 4WD grip in all but the slipperiest situations, no levers or buttons to flick, until it gets really slippery.
Disadvantages: Isn't truly 4WD on low traction surfaces when left to its own devices (unless traction control or locking/limited slip diffs are also fitted).
Selectable 4WD
A full-time 4WD system that you can choose to drive in either 2WD, like a part-time 4WD, or full-time 4WD on paved surfaces.
Advantages: Best of both worlds.
Disadvantages: Complex system.
On-demand 4WD
Takes the best of part-time and full-time systems and attempts to combine them in a foolproof, user-friendly system. No 4WD expertise is required. Basically, the car runs in two-wheel drive until the system (which can be electronic, hydraulic or a combination of both) senses that one axle is spinning faster than the other and shuttles power to the 'dead' axle.
Advantages: Less drag on components, potentially allowing better performance and economy than full-time; user-friendly.
Disadvantages: Some systems are slow to engage 4WD and are complex (read: expensive) should it all go wrong.