
The main implication of this theory is that we can only have a picture of the world we live in to a limited extent. We cannot say what happens beyond that limit, what was the exact energy and position of that electron before we observed it, how the atomic nucleus and subatomic particles really look like, and even cannot be sure that these things we call particles had existed at all before we engaged in their direct observation. Bizarre. Not only for us, but also for the physicists of the era when Heisenberg came up with this idea about the limitations of our observations. Since then the scientific society has been eager to prove that Heisenberg was wrong - without any success. Today's hot news on the issue is that the precise predictions of the principle still hold without any doubt. Read more about the current debate and the new findings here.
(For contemplators lost in Wikipedia's articles on modern physics, I would recommend the brilliant book of John Gribbin, In Search of Schrödinger's Cat)