Short answers, pulled from the story.
The Apollo Guidance Computer provided computation and electronic interfaces for guidance, navigation, and control of the Apollo spacecraft. It was installed on both the Apollo command module and the Apollo Lunar Module, and it controlled the flight during most mission phases, with astronauts flying manually only briefly during lunar landings.
The AGC is recognized as the first computer based on silicon integrated circuits. Its Block II version, which flew on crewed lunar missions, used around 2,800 ICs supplied by Fairchild Semiconductor, implemented using resistor-transistor logic in a flat-pack configuration.
The alarms were caused by a flawed interface control document that failed to specify phase synchronization between two 800-Hz signals used by the rendezvous radar and the computer. The random phase offset made the stationary radar appear to be rapidly shifting position, generating about 6,400 spurious cycle steals per second and overloading the processor. Guidance controller Steve Bales and team member Jack Garman issued GO calls, and the AGC's priority scheduling automatically shed lower-priority tasks to complete the landing.
Software development on the AGC consumed 1,400 person-years of effort at its peak employing 350 people. Key figures included Margaret Hamilton, who oversaw implementation of the lunar mission programs; Frederic Martin, who led COLOSSUS for the command module; and George Cherry, who led LUMINARY for the lunar module. The operating system design was created by J. Halcombe Laning.
The DSKY, pronounced DISS-kee and standing for display and keyboard, was the user interface through which astronauts communicated with the AGC. Commands were entered as two-digit Verb and Noun pairs on a calculator-style keyboard, and results appeared on green electroluminescent seven-segment displays. The command module carried two DSKYs; the lunar module had one.
Margaret Hamilton received the Presidential Medal of Freedom in 2016 for her role in creating the Apollo flight software. She led the team that implemented the details of both the COLOSSUS command module software and the LUMINARY lunar module software, and she was particularly focused on anticipating human-error scenarios in astronaut-computer interaction.