Techno-futurist poster boys like Ray Kurzweil and Hans Moravec have long predicted that increasing processor capacity will inevitably lead to "strong AI", and soon. But they overlooked the truth of computer science that making software do what you want is much more difficult than building the necessary hardware. Of course, one way around this is to emulate existing software on new hardware, and it looks like there is interesting progress in that direction.
What will it mean if we are able to effectively simulate a human brain in a computer, so that the mind actually works? The practical implications are huge: immortality for the simulated minds, cloning minds, potentially much faster cognition, easy long-distance space travel, some scary consequences for the simulatee if the machine is compromised. But it's unclear if we'd be able to make fundamental improvements to the capabilities of human cognition. We are dealing with an exceptionally large and strange piece of legacy code.
Philosophically, it would be a blow against some forms of dualism. That doesn't bother me because personally I'm not much of a dualist. I grew up with the assumption that the mind is what the brain does, and becoming a Christian did not require me to change that. God knows everyone's mental state at all times, so resurrection only requires that state to be copied into a new body. Any consciousness in the interregnum can be achieved by God doing the necessary processing himself. (Better thinkers than I have speculated along these lines.) The idea of a soul independent of the body that carries on on its own is not required in the Bible, as far as I can see, although the Gnostics probably would held it.
I doubt we're anywhere close to actually achieving the simulated brain, however. We should expect many iterations of discovering that there's some subtle but important phenomenon not being simulated. And who knows, maybe Penrose will turn out to be right and some quantum phenomena turn out to be important...