A graph like this is one of the more common ways to show the dangerous escalation of the Cold War and nuclear weaponry. As I said, it's an oft repeated trope to talk about how these nukes are enough to make something like 7 or 8 Earths uninhabitable if they were used. To me that kind of begs the question as to why, say, the Soviet Union felt the need to add tens thousand more warheads rapidly from the 60s to the late 80s. Its not like you can destroy planet Earth more than once, so what was the utility in building and maintaining such a large stockpile, that presumably you'd never want to use, and if you did use them you'd probably only have one shot to do so? Could they not have recycled nuclear material and to a lesser extent warheads to new designs as technology improved and dismantled their old ones, maintaining a fairly constant amount over time?
Warheads were stockpiled for redundancy against countermeasures and resiliency against a surprise attack.
On the offensive side of things, the idea was to have enough warheads to overwhelm any defenses that may be present. That often meant that a single target would be targeted by multiple warheads with the idea that a certain percentage would get through and destroy the target. There were also different means of deploying warheads that accomplished different effects. A good example is a very high altitude detonation. Such detonations have a number of effects caused by the way the explosion interacts with the upper atmosphere, including an electromagnetic pulse (EMP). While the impacts of an EMP often get overblown when it comes to tactical effects - military ground equipment was generally hardened against the effects - the EMP would create a large amount of radar noise that would effectively blind enemy early warning radar networks at the distances they'd be intended to work. In practice, that meant that an attacking party might kick off an exchange by detonating a number of warheads at high altitudes along the path that friendly warheads would be taking, blinding early warning radars and reducing the effectiveness of missile-defense networks. On a more tactical or operational level, high altitude airbursts could be used to reduce the effectiveness of conventional air defenses with the same kinds of radar effects. The Soviets, for example, had plans for a combination of conventional and nuclear strikes for their air war over Germany should the Cold War go hot that hinged on high altitude airbursts, tactical nuclear strikes on command and control centers and airfields, and a heavy reliance on jammer/chaff-laying aircraft to help clear a corridor for strike aircraft.
Even when we get to more conventional use of nuclear weapons, hardened targets may often require multiple warheads to effectively destroy. Traditionally, we think of airbursts when we think of nuclear attack, as they're the most efficient way to spread the energy over the widest possible ground area. However, targets are often hardened against nuclear attack, making air bursts less effective. A common way to do so is to sink a potential target into the ground - something we see with missile silos or the NORAD headquarters in Cheyenne Mountain. In these cases, ground bursts - where the warhead detonates on impact or after penetrating some distance under the ground - are used. As a ground burst less efficiently distributes its force, it often means that larger hardened targets are going to require multiple warheads to totally destroy.
The defensive side is largely the reverse. You want to keep warheads survivable so that you can effectively retaliate against a first strike. That means spreading warheads across launch platforms, distributing launch systems and critical infrastructure to require the maximum number of warheads to get the desired effect, and, most importantly, deploying as many warheads as possible. The end result is deterrence. The defending power just needs to ensure that a successful first strike by the adversary is unlikely enough to prevent an effective retaliation that the enemy won't feel comfortable considering it.
On the more active defensive side, warheads were often deployed as part of defense networks. US missile defense systems like Nike Zeus and Sprint were deployed with fairly sizable nuclear warheads themselves, the idea being that it would make up for lower accuracy and, with larger warheads like the proposed 400kt W50, even take out clusters of incoming weapons if timed right.
