At some point in the future we may be able to scan someone's brain at very high resolution and "run" them on a computer.  When I first heard this as a teenager I thought it was interesting but not hugely important. Running people faster or slower and keeping backups came immediately to mind, and Wikipedia adds space travel, but those three by themselves don't seem like they change that much. Thinking speed doesn't seem to be major limiting factor in coming up with good ideas, we generally only restore from backups in cases of rare failure, and while space travel would dramatically affect the ability of humans to spread  it doesn't sound like it changes the conditions of life.
This actually undersells emulation by quite a lot. For example "backups" let you repeatedly run the same copy of a person on different information. You can find identify a person when they're at their intellectual or creative best, and give them an hour to think about a new situation. Add in potentially increased simulation speed and parallelism, and you could run lots of these ones looking into all sorts of candidate approaches to problems.
With emulations you can get around the mental overhead of keeping all your assumptions about a direction of thought in your mind at once. I might not know if X is true, and spend a while thinking about what should happen if it's true and another while about what if it's not, but it's hard for me to get past the problem that I'm still uncertain about X. With an emulation that you can reset to a saved state however, you could have multiple runs where you give some emulations a strong assurance that X is true and some a strong assurance that X is false
You can also run randomized controlled trials where the experimental group and the control group are the same person. This should hugely bring down experimental cost and noise, allowing us to make major and rapid progress in discovering what works in education, motivation, and productivity.
(Backups stop being about error recovery and fundamentally change the way an emulation is useful.)
These ideas aren't new here  but I don't see them often in discussions of the impact of emulating people. I also suspect there are many more creative ways of using emulation; what else could you do with it?
 I think this is a long way off but don't see any reasons why it wouldn't be possible.
 Which has a big effect on estimates of the number of future people.
 I think most of these ideas fo back to Carl Schulman's 2010 Whole Brain Emulation and the Evolution of Superorganisms.
I also posted this on my blog