Alexander Pierce is a high ranking HYDRA member who has infiltrated the World Security Council. Before the events of the film, during a mission in Bogata, Pierce met SHIELD agent Nick Fury, who saved several lives including his daughter. Surprised by Fury's actions, Pierce went on to appoint Fury as the director of SHIELD.
Several years later, the HYDRA influence over SHIELD has increased, and a trio of Helicarriers are built under 'Project Insight.' They were meant to form a SHIELD security network to protect the world. But secretly, HYDRA wanted to use them to kill and target over 20 million people that were selected by HYDRA scientist Arnim Zola's algorithm, which means that any individual that posed a threat for HYDRA would be irrelevant to HYDRA's new world order.
After his discovery of a SHIELD arsenal by Georges Batroc, which was really planned by Fury, Pierce initiated the Winter Soldier to assassinate him. But after an attack by the Winter Soldier, Fury retreated to Steve Rogers' apartment and tells him not to trust anyone because he realizes that SHIELD has been compromised before (seemingly) being fatally shot by the Winter Solider..
Following the apparent death of Fury, Pierce meets with Rogers and thinks that he has hidden something. Pierce afterwards sends agent Brock Rumlow and his team to capture Rogers, who rendezvous with Black Widow for help. He assigns the Winter Soldier a new objective to assassinate Captain America and Romanoff. After an investigation on HYDRA sleeper agent Jasper Sitwell for the real point behind 'Project Insight', Captain America, Black Widow and their ally Falcon get captured by SHIELD, but it turns out they get rescued.
Proceeding with his plot, Pierce meets with the World Security Council members to activate 'Project Insight'. But unknown to him, Rogers and his team infiltrate the Triskelion and they reveal HYDRA's true motives motivating every good SHIELD agent to stand up against Pierce, Rumlow and his STRIKE team. As Captain America and Falcon infiltrate the Helicarriers, they change the targets according to Zola's algorithm and turn the Helicarriers into the targets. While this goes on, Black Widow rescues the hostage World Council members and forces Pierce to help her and the seemingly alive Nick Fury to unlock every SHIELD/HYDRA secret and upload them all to the Internet.
After the destruction of the Helicarriers and HYDRA's secrets are released on the Internet, Pierce uses a small remote-controlled incendiary device to kill the other council members and threaten Black Widow, which was his way of forcing Fury to let him flee. But Black Widow disables the explosive, which gives Fury the opportunity to shoot him dead. Pierce's dying words are "Hail HYDRA."
A younger Pierce makes an appearance in the show during a flashback to 1989. During this year, Pierce sent two agents to release Werner Reinhardt, a former member of HYDRA that was sentenced to life imprisonment by Agent Carter.
In the comics, Pierce is a much younger field agent. Robert Redford let slip that he accepted the role because he wanted to portray a villain; it turns out the movie version of Alexander Pierce is a combination of the Alexander Pierce from the comics and Aleksander Luvkin, the man responsable for the creation of the Winter Soldier. 
In an interview with USA Today, Samuel L. Jackson revealed that Alexander Pierce is a member of the World Security Council, but was not present during the Avengers.