What does it mean when a coral is said to be peaceful, semi aggressive and aggressive? Also how is each one handled?
Unless it's fire coral or something that comes with similar handling-warnings, most corals don't cause any kind of reaction in most people. Some of the more aggro corals may cause welts against sensitive skin in sensitive people.
Mostly, however, those levels refer to how much of a problem they're going to be with other corals. For example, GSP and Xenia aren't aggressive. They're invasive, but practically anything else with longish tentacles can burn them back. Favia and Euphyllia corals can be extremely aggressive, with long sweeper-tentacles with powerful stings that'll really screw up less aggressive species. Even Kenya Trees can be extremely aggressive, but they don't have much reach and don't seem to vomit up their mesentaries to attack other corals like some do.
Basically, if you have an invasive, nonaggro coral, it'll be beaten back by more aggressive species. If you have a noninvasive, agressive coral, it'll hold back less aggressive species. If you have an invasive, aggressive coral, you're screwed.
In many cases, certain highly aggressive species of the same genus (all Euphyllia species, for example, and certain groups of acans) can be placed near eachother and won't sting or inhibit eachother. Management of these interactions can be useful to 'corral' certain invasive, but easily suppressed, corals.
In some cases, it doesn't matter that a coral is highly aggressive (acans) because they have extremely short reach and well-behaved growth forms. So long as they're not brushing up against something, it's not gonna be a problem. In other cases, you need to run carbon because one or more of your corals are waging chemical warfare against your whole tank. (Many soft corals.)
In short -- those levels are a really, really rough guidline that needs to be supplemented with an understanding of the coral's physical properties, growth habits, and suppressive strategies.