Trust. It is what every healthy relationship is built on. There are a million ways you break your partner's trust, but the most common way is cheating. It is estimated that 30-60% of married people will cheat on their partner within the course of their marriage.
So the question is, is cheating a deal breaker or can you fix the relationship? The answer is not an easy one and won't be the same for everyone. It is going to take two people who both really want to make the relationship work and to put in a ton of effort.
The most important thing for the cheater to remember is that although your partner is choosing to forgive you, it will take time for them to do so. Be prepared to be asked a million question as your partner struggles with accepting what has happened. They will not trust you and you can not be upset about it. You have to let them forgive you in their own time.
As for the cheated on, you have to remember that you are agreeing to forgive and move forward. You are not going to get over this right away and it will hurt, but you can not hang on to a grudge for too long. This will only cause you bitterness and resentment towards your partner. You are trying to wipe the slate clean and start over.
When it comes to infidelity, reconciliation is not always the right answer. You have to sit down and make sure that you two both want it and are on the same page. You have to get to the root of the problem and why it happened. This way you prevent it from occurring again.
Do what is best for you and your partner. This is not a problem that any one else can tell you how to fix.