Decompression Illness is a designation covering two types of injuries that a diver can get in connection with breathing compressed air at depth.
Decompression sickness (DCS) covers injuries related to the absorption and release of Nitrogen into body tissues: If Nitrogen is absorbed and subsequently released too quickly, it can cause bubbles, which can cause all sorts of problems: In general, bubbles in your bloodstream is Bad News. DCS can be avoided by using dive tables (or a dive computer) conservatively, and ascending slowly (18 meters per minute or 9 meters per minute, depending on whether you are using PADI's recreational dive planner dive tables, or the US Navy dive tables, respectively). DCS symptoms generally manifest between 15 minutes and 24 hours after surfacing from a dive.
The other type of injuries is lung over-expansion injuries. These can occur when a diver holds their breath whilst ascending. The expanding air in their lungs causes one of four different injuries - but all are dangerous and need immediate medical help. Lung over-expansion injuries manifest immediately after a dive, and can be avoided by never holding your breath whilst breathing compressed air: You should always in- or exhale when scuba diving.
The reason why the two very different illnesses are lumped together under Decompression Illness, is that they both have the same ground cause (breathing compressed air at depth), and the treatment is the same for both: the ABCD's of first aid, and 100% oxygen administered, plus seeking expert medical advice.