Destroying the legs reduces the unit's movement to one per turn - de facto immobility. And if you're lucky enough to blow out the torso, the whole unit goes down, regardless of the status of the other limbs. Well, as noted before, attacks impact on each of the four areas randomly, so you often need to hope for the best when making your attacks and pray that all enemy attacks hit your legs. Later on, you can develop a variety of special Skills - like Aim, which give you the option to aim your attacks wherever you please. There are other types of Skills which allow pre-emptive strikes or special effects upon weapon impact, but the Aim skills are the ones that actually matter.
Weapons come in three main stripes.
There are Long-range weapons like missiles and bazookas. These have dodgy hit rates but hit from a long range, which is Good. There are Short weapons, which have ranges of one or two squares, and usually come in the forms of machine guns, rifles, or my personal favorite, flamethrowers. Last come Melee weapons, usually tonfas, little metal sticks that your Panzers whack enemies around with. Back-up weapons include repair items, shields to protect you from harm, and grenades that theoretically blind the enemy or protect you from missile attacks, but have never done a damned thing for me.