The idea that marrying someone who is divorced may be adultery comes from two things Jesus says:
“Everyone who divorces his wife and marries another commits adultery, and he who marries a woman divorced from her husband commits adultery.” Luk 16:18
“It was also said, ‘Whoever divorces his wife, let him give her a certificate of divorce.’ But I say to you that everyone who divorces his wife, except on the ground of sexual immorality, makes her commit adultery, and whoever marries a divorced woman commits adultery. Mat 5:31-32
In both passages, Jesus is calling people to cast sin far away from their lives, to do whatever is required. In the same passage, Jesus says:
“You have heard that it was said, ‘You shall not commit adultery.’ But I say to you that everyone who looks at a woman with lustful intent has already committed adultery with her in his heart. Mat 5:27-28
So, in fact, by Jesus standards, it is very easy to commit adultery, and very hard not to. And by these standards, marrying a divorced person is adultery, since they have broken their commitment to their first partner, concerning which Jesus says:
What therefore God has joined together, let not man separate.” (Mat 19:6)
Note that many people have claimed that marriages which are formed under such circumstances (e.g. one of the partner has previously been married, with or without prior adultery), are invalid, and must be broken apart. Previous BibleQ answers deal this with this:
In our family Bible that commandement was changed by my Great Uncle Professor Septimus, a great scholar of Greek and Aramaic. Septimus beleived the commandemnt was an injunction to commit adultery – and a condemnation of divorce as uneccessary. He said God originally condemned men and women who let themselves get out of shape and unattractive as they were less desirable to watch at Chaldeab and Jebusite Orgies which God truly relished.
In our family we have never had a divorce.