The idea is basically fairly simple. Instead of releasing CarbonDioxide from the Combustion of Fuel, it is washed out immediately afterwards and then stored somewhere else. The key places tend to be underwater or under rocks. Storing under water seems counter-intuitive, but at pressure, CarbonDioxide turns into a stable solid. Over time it will dissolve out, but it's not that soluable so this takes quite a lot long time.
This is not a bad idea, but it's a half and half strategy. Firstly, it still relies on FossilFuels, which are NonRenewable. Sooner or later they will run out. Secondly, it only gets rid of the problem. The best techniques for CarbonCapture put the problem of for a pretty long time (1000 years maybe), but at the Carbon is still in a low complexity, that is CarbonDioxide. Unless you produce complex Organic compounds or solid Carbon—like Coal—this release is always going to happen.
Having said all of this, CarbonCapture is a lot better than just releasing CarbonDioxide into the atmosphere. And it will have a much smaller requirement for changes in Energy production technology. The worse can scenario is, however, that use of CarbonCapture technology will enable us to put of the main issue—how to extract Energy from Renewable sources.