To believe something completely (often without sufficient evidence); to be firmly convinced. Can also imply being taken in by someone.
彼は彼女の言葉を何の疑いもなく信じ込んでいる。
He believes her words without any doubt.
うその情報を信じ込んで大金を失った人がいる。
There are people who lost a lot of money after believing false information.
専門家の言葉を安易に信じ込むのは危険だ。
It's dangerous to uncritically accept what an expert says.