The Spectres are a group of elite agents in the Mass Effect universe. The name "Spectre" is an abbreviation of the words "Special Tactics and Reconnaissance".
The Spectres are formed of various species chosen by the Citadel Council to uphold galactic stability at any cost. Spectres frequently operate individually and they are free to do whatever they want to accomplish their missions and are not held accountable to any laws. Although they do answer to the Council, they usually turn a blind eye to the actions they take. Currently only 4 Spectres have been met in the Mass Effect games, Commander Shepard, Nihlus Kryik, Saren Arterius, and Tela Vasir. All of whom have died at some point or another, although with Shepard's revival at the start of Mass Effect 2, he is the only one still living. It is estimated that there are less than 100 Spectres in active duty.
The Spectres were founded shortly after the Salarians joined the Asari on the Citadel Council and was initially made up of the best Salarian STG operatives and Asari huntresses. The Council was worried about the quick pace that the Krogans were spreading and colonizing the galaxy after the Rachni Wars. This lead to the Krogan Rebellions, but the Spectres were ready for them and covertly sabotaged and destroyed many of their facilities and plans with the use of guerilla style tactics, until the Turians joined the war. Initially the existence of the Spectres was secret, but after the successful quashing of the Krogan Rebellions their existence was admitted to the galaxy.
The first potential Human candidate to become a Spectre was David Anderson. The Spectre put in charge of his evaluation was Saren Arterius. During their first mission together, however, Saren blamed him for the death and destruction of a mining camp and facility even though these were the results of his own actions. Saren's final report ruined Anderson's chances of ever becoming a Spectre. The story of this mission is covered in the first Mass Effect spin-off book Mass Effect: Revelation.
In the first Mass Effect game, you play the role of Commander Shepard who has been selected as a possible Spectre candidate. Nihlus Kryik is sent to evaluate you on a number of missions which you will work together. Unfortunately, Nihlus meets his end at the hands of Saren Arterius on your first mission together on Eden Prime. Saren is the Council's top Spectre agent, but he has gone rogue and has chosen to help bring the Reapers back to the Galaxy. Thinking their return is inevitable, Saren believes he can show them that organic life can be useful to them, and convince them not to wipe out all intelligent civilization, as they've done so many times before. Little does he know but his thoughts and twisted logic are all the result of the Reaper indoctrination by Sovereign. Commander Shepard proves Saren's betrayal to the Council with the help of information obtained by Tali'Zorah nar Rayya and becomes the first ever Human Spectre. Shepard is then forced to stop Saren and the Reaper plans, thus saving the galaxy, becoming potentially the most famous Spectre as well.
Mass Effect 2
In DLC for the second Mass Effect game, called "The Lair of the Shadow Broker" we meet the fourth Spectre Tela Vasir. She initially helps you in your investigation to find Liara T'Soni but eventually turns out to be an agent of the Shadow Broker and an assassin sent to kill Liara. She is killed in the following fight by Commander Shepard, but she claims she's doing what needs to be done to protect the Shadow Broker as he has given her intel which has saved many lives in the past and aided her in upholding justice throughout the galaxy as a Spectre.