In the book, a Soviet sub commander Marko Ramius (the book was originally published in 1984) is planning to defect to the US with his sub and entire crew to the US. Both he and his crew are becoming frustrated and disillusioned with the Soviet government for different reasons.
His crew is starting to have their doubts about the political and economic views of the Soviet Union, and are starting to feel unappreciated by the Soviet Navy. Commander Ramius is starting to have his own philosophical issues with the Soviet government, but in a much different way: their views on religion and the afterlife.
Shortly before this plan was put into play, Commander Ramius' beloved wife, Natalia, died in a hospital during what should have been a routine appendix removal surgery due to the inefficiency and downright incompetence of the medical staff, and the medical system. Several unfortunate events led to her death, including a surgeon who showed up to work drunk, and spent several minutes with an oxygen mask on before the surgery to try and become more alert.
In his grief, he starts to lean on the Catholic faith that his grandmother, a woman who grew up in Lithuania in the pre-Soviet era, tried to raise him with. It's unclear whether he has fully converted back to Catholicism, but he is starting to head in that direction, he is starting to doubt Soviet doctrine, and is hoping that his grandmother was right all along. He is angry at the Soviet system for not only taking his wife from him prematurely, but he feels that they are trying to rob him of his memories of her, and the hope he is trying to cling to that he will see her again in the afterlife.
It is in these scenes that Tom Clancy's views on religion become much more clear, I had always suspected that Clancy was a religious man, probably a Catholic fundamentalist, and after looking up information about him online, it appears I'm right. I'll let Clancy's own words speak for themselves, though:
Marko Ramius watched the coffin roll into the cremation chamber to the somber strain of a classical requiem, wishing he could pray for Natalia's soul, hoping that Grandmother Hilda had been right, that there was something beyond the steel door and mass of flame. Only then did the full weight of the event strike him: the State had robbed him of more than his wife, it had robber him of a means to assuage his grief with prayer, it had robber him of the hope --- if only an illusion --- of ever seeing her again.(Emphasis placed on the text by Clancy, not me).

