While there is no consensus on how to define the term "terrorism", terrorists are generally considered to be people who express their ideals through violence. For example, don't like the president? Kill him! A terrorist commits terrorist acts or acts of terror that go from sabotage to going on an all out killing spree to deliver their message. They may also be called rebels or freedom fighters.
A terrorist is usually part of a terrorist organization that organizes and plans attacks. This allows the terrorists to plan out attacks all over the world and makes them extremely hard to catch. They're well armed and well trained. They use a wide array of weapons and explosives and are prepared to die for their cause.
Terrorism often goes hand in hand with guerilla warfare tactics, in an attempt to even the playing field during asymmetric warfare, where non-state rebel groups are heavily out-gunned and out-numbered by heavily armed, well-trained, state military forces.
Some of the more well known real-life rebel groups that have at various times been labelled as "terrorist" organizations include Vietnam's Viet Cong, Ireland's IRA, South Africa's ANC, Palestine's PLO, Sri Lanka's Tamil Tigers, Afghanistan's Mujahideen/Taliban, and Tibet's TYC.
Ironically, while the term "terrorism" now often refers to non-state rebel groups, the term "terrorism" (from French "terrorisme") was originally coined to specifically refer to state terrorism (where governments carry out acts of terror), not the non-state terrorism that the term often refers to today.
In most games, especially military shooters, you have to stop the terrorists from getting hold of a superweapon and spreading chaos across the world. In some multiplayer games like Counter-Strike, one team plays as the army, the others as the terrorists. In some games, such as The Saboteur or the Red Faction franchise, you are a terrorist, fighting violently against an established government, even if it is a corrupt and evil one.
In contrast to many shooters where terrorists are often portrayed as villains, the role-playing game genre (particularly Japanese role-playing games) often tends to portray terrorists as anti-heroes. One of the most notable examples of this is Final Fantasy VII, where the terrorists (in this case the eco-terrorist group Avalanche) are the heroes and the government (controlled by a corporation called Shinra) are the villains. More generally, many of the Final Fantasy games often involve heroes that are seen as terrorists / rebels / freedom fighters, facing off against a corrupt government or empire. Beyond role-playing games, the Metal Gear series of stealth action games also tends to portray terrorists / rebels / freedom fighters in a more sympathetic light, like with the hero-turned-terrorist Big Boss or president-turned-terrorist Solidus Snake.