The early Cold War strategy was to rely on massive nuclear forces to deter even conventional action. This was Eisenhower's "Massive Retaliation" policy: any military aggression by the USSR would trigger a huge, nuclear response.

But by the end of the Eisenhower administration, this became seen as problematic and potentially "non-credible" — that the threat might not be acted upon. Why not? Once you get into a situation where the Soviets have a nuclear capability that they can use, you are in a much trickier situation. If the Soviets moved into West Berlin, would that be worth endangering all of Europe, or American cities? Or to put it another way, if you're a European, what are the odds that the USA is willing to trade New York for West Berlin?

Deterrence threats need to be "credible" to be effective (so the strategic thinking goes) — otherwise you are in the familiar situation of a parent who threatens a child, but the child knows that the parent will not follow through on the threat, and so the threat has little to no meaning.

In situations like these, a conventional force, and tactical nuclear weapons ("limited" nuclear war), start to look like they increase credibility. Maybe threatening total thermonuclear war in response to Soviet conventional incursion in West Berlin seems unlikely... but if there were conventional forces there, would they fight back? Probably. Might they use tactical nuclear weapons in a limited way to defend against military combatants? Perhaps. So now, in theory, that sort of thing looks less profitable to the Soviets — and more dangerous, as well, since small conventional fights, much less tactical nuclear strikes, might "escalate" into all our nuclear war. So from two angles this reinforces the deterrent: it promises some kind of appropriate response (so the options are no longer "nuke everyone" or "do nothing"), but that appropriate response presents a plausible path to total destruction ("escalation"). So, in theory, this makes Soviet action along these lines seem pretty undesirable.

I am glossing over a lot of differences in thinking and doctrine that evolved from the period of the early 1950s through the 1960s, and to be sure the doctrine is never "stable" on any of these points. Separately it is worth noting that a large part of US deployments to Europe are also about reassuring NATO allies that the US has "skin in the game" in Europe, and that it would not just turn a blind eye to Soviet aggression (or get into a situation where it felt that it could write-off Europe easily). The diplomatic and strategic angles are fairly complex.

A nice overview of the strategic thinking is Lawrence Freedman, The Evolution of Nuclear Strategy, which gets into the motivations and nuances between, say, "Massive Retaliation," "New Look," the "New New Look," and other strategic policies. It is important, as the title of Freeman's book emphasizes, to see the strategic dimension as a line of thought that "evolved" over time (reacted to changing circumstances, sometimes went down blind alleys, etc.), and not see it as somehow transcendental and "fixed" (as often people tend to these days, as if the bomb just made its strategy obvious to people).