Star Wars is an Anti-Ballistic Missile (ABM) system that was proposed in the 80's. It's implementation was not only going to be prohibitively expensive, but the technology needed didn't really exist in a useful form at the time. It's often seen as a PR attack on the Soviets, to try and get them to spend more money on defense.

Also, it was in direct violation of the ABM Treaty signed between the US and the USSR in 1972. The theory is that if any side that gains a reliable defense against nuclear attack, the whole MAD doctrine (Mutual Assured Destruction) falls apart. After all, if you can launch your weapons without fear of retaliation...what's to stop you from launching your weapons? And if the other side is developing such a defense, then you may feel your only recourse is to launch before they get it up and running.

We've since withdrawn from that treaty (which the Russians count as one of a string of provocations from the West in recent years). But shooting down ICBM's is still a difficult task. Our current and planned interception systems are designed to stop an attack from a rogue state with a small arsenal. It's easier to track and shoot down two or three ICBM's than two or three thousand.