More specifically, that Jaime will be the one to kill Cersei before dying himself.
Although many believe Daenerys will take after her father and become the Mad Queen, according to this theory, it will actually be Cersei who follows in Aerys's footsteps. People think she'll go mad and try to destroy King's Landing with wildfire – and Jaime will kill her just as he did Aerys. He will then either kill himself or die in the wildfire. It sounds kinda crazy, but there's actually some solid evidence that this will happen...
Like the Mad King, Cersei is quite paranoid, seeing enemies everywhere and seeking to destroy them before they destroy her. A lot of her paranoia stems from a prophecy she received as a young girl from a character called Maggy the Frog.
The full prophecy predicted that:
* Cersei wouldn't marry a prince, but a king. At the time of the prophecy, Cersei expected to marry Prince Rhaegar Targaryen. But he later married Elia Martell and then was killed by Robert Baratheon, who became king – and Cersei's husband.
* The king would have 20 children (16 in the books) and Cersei would have three. As we know, Robert had many bastards (including our beloved Gendry), while Cersei had three children to Jaime: Joffrey, Myrcella, and Tommen.
* A younger, more beautiful queen would take all she holds dear. This part of the prophecy helps explain her distrust of Sansa and Margaery. Margaery seems the most likely candidate to fulfill it (her marriage to Joffrey led to his death, and she has more power over Tommen than Cersei does – plus Cersei's attempts to thwart her ultimately led to her own arrest). But Daenerys could also swoop in and really destroy Cersei.
* Cersei's children would wear crowns, and die before her. Joffrey became king and then died. Myrcella was a princess, betrothed to the prince of Dorne, and is now dead in the show (although she's apparently still alive in the books). Tommen is king and still alive...for now.
* Cersei's grief will "drown" her, and then the "valonqar" (High Valyrian for "little brother") will strangle her to death. Cersei is growing increasingly unstable (especially in the books), and there's no doubt the death of Tommen – her last remaining child – would push her over the edge into madness and metaphorically drown her. As for the "valonqar" – Cersei has always believed it to be Tyrion, but Jaime is also a good candidate, being born just after her.