In
nuclear planning parlance, the process of increasing a structure or object's resistance to nuclear weapon effects. In the nuclear targeting biz, targets (such as
missile silos) are described in
p.s.i. of hardness; that is, they are rated by the amount of
static overpressure and
dynamic overpressure they can withstand. If you know the weapon you are using, this value can easily be converted into the maximum 'miss distance' that you can allow before you must consider the target 'undamaged' for targeting and weapon
allocation purposes. Typically, such measures are only concerned with whether the structure is usable (for example, if you can launch the missile inside a
silo successfully afterwards). Note that in the case of missile silos,
command centers and other extremely hard targets, it is likely that
nuclear weapon effects other than overpressure or contact with the fireball will, in the process of reinforcing the structure vs. those two, be adequately shut out.
One reason the U.S. (and, presumably, the U.S.S.R.) had decided they needed such outlandish numbers of nuclear weapons was because defense planners, being inherently conservative, tended to assume (and still do) that enemy structures are much harder than they actually are. After all, if you're wrong and you assumed it was harder than it was, all you've done is increase your chances of destroying it; however, if you assume it's weaker than it is, then your allowable miss distances get smaller rapidly.
Unfortunately, a linearly-decreasing allowable miss distance means an exponentially increasing number of shots are required to achieve the same probability that one of them will land within the miss distance (for more information, see probability of kill (Pk)). So, you find yourself allocating more and more weapons to each target for each small incremental increase in the assumed capability of the enemy.
Hardening doesn't always refer to targeting; systems and weapons can be hardened against nuclear effects to increase survivability in a nuclear environment, the U.S. Military's favorite euphemism for too damn close. Satellites and aircraft can be hardened against Electromagnetic Pulse, ships can be hardened against prompt radiation to increase crew survivability, and so on. At the other end of the scale, nuclear warheads can be hardened to improve their chances of surviving long enough after being dropped into a recently-hit area to detonate properly.