Basically as Shude has said the engine is de-tuned by the manufacturer to take into account the variety of fuels available in the world, the emissions regulations and so on. Because they take the lowest common denominator when doing this there is quite a large 'tolerance' level built-in to many of the boost and fuelling parameters. The well regarded tuners will amend some of the fuel and boost 'maps' in your car to take account of those tolerences and subsequently release more power that the engine is quite capable of delivering.
Just to expand a little further a map is a table of values for a particular function that tells the engine what to do for a specific load/rpm level. So for example - if the throttle is wide open and the revs are at 2500 then inject a given amount of fuel to continue the acceleration to the next point on the map which moght be 2550rpm and so on. There are quite a few maps to take account of different scenarios such as light throttle, cruising etc and for when there isn't a map the ECU can guess a value in between.
Most re-maps are safe in that they don't put the engine under too much stress. If they did then the built-in 'alarm' systems would put the engine into 'safe' mode. i.e. low boost to enable you to get to a garage. There are examples of tuners who do stretch things and reach those limits which can be frustrating, but you'll find that most of the reputable guys don't have any issues.
Be aware that any re-map will invalidate a manufacturers warranty and you may have to revert to their own warranty if a problem does arise.