"Oh! Hey, look, it's like the glowy thing!" "That "glowy thing" is an explosive Chitauri Energy Core." "Whoa... whoa, whoa, whoa! You mean we've been carrying around a bomb?! "It would require radiation to transform it into an explosive state."
The Chitauri Energy Core is the energy source for most of the Chitauri weapons. Originally used exclusively by the Chitauri, the weapons left behind after the Battle of New York allowed citizens of Earth access to these cores.
When Spider-Man stopped an arms deal between Aaron Davis, Herman Schultz, and Jackson Brice, he wound up chasing Brice and Schultz through the suburbs, knocking away one of the weapons the van carried in the process. After being rescued by Iron Man, he came across the weapon and later took it apart to retrieve the core inside, dubbing it "The Glowy Thing". Schultz and another thug later searched for the missing weapon but were unsuccessful.
Spider-Man brought the core with him to Washington DC in order to locate the arms dealers, but left it with Ned in the hotel room when he went to apprehend them later that night. When confronting the Vulture, he knocked himself unconscious inside the truck and was unknowingly taken to the D.O.D.C. Vault. Initially deciding to wait it out until the doors opened in the morning, he quickly became desparate 37 minutes in, searching the storage unit he was in to find anything he could use to break himself out. In his search, he found another core. Initially regarding it with curiosity, he became frantic when he learned from Karen that exposure to radiation made it explosive and that, in essence, they had been in possession of a bomb, trying and failing to relay the news to Ned.
After managing to escape the vault, Spider-Man was finally able to reach Ned, but was interrupted by Liz before he could tell Ned about the core. Unfortunately, the core passed through the Washington Monument's security checkpoint and was bombarded by X-Rays and infrared radiation, causing it to destabilise. The core eventually detonated in Ned's backpack, causing severe structural damage to the Monument. Thankfully, Spider-Man was able to rescue the occupants of the elevator before anyone sustained severe injuries.
When Spider-Man prevented Vulture from hijacking a Stark Industries plane loaded with artifacts from the Avengers and steering it into a beach on Coney Island, he sustained severe injuries and could not fight back as the Vulture brutally beat him, but was left in favor of the arc reactor cores in one of the storage boxes. However, he had already sustained severe damage to his Exo-Suit, and the arc reactors were emitting radiation, setting off the cores in his wings and causing the suit to explode mid-flight. Before he could die however, Spider-Man saved him from the wreckage.
The Chitauri Energy Core's main function is to serve as a power source, powering most, if not all of the Chitauri weapons. Additionally, if tampered with Earth's tech, it can power hybrid weapons. However, if the Chitauri core is exposed to radiation of any kind, the core will become explosive, eventually detonating to catastrophic effect.