The letters of transit were a kind of legalized certificates that allowed the people who possessed them to leave Casablanca and travel freely. They were priceless to anybody, except for Rick. Victor aspired to acquire those letters so that he and his wife could go to New York. They are endangered here in Casablanca as Victor is a famous Czech Resistance leader and was hunted by the Germans. Without the letters, there was no way the couple could escape to America and that meant death to Victor. Moreover, there is no way he could acquire a normal visa, since the German officers would not allow anybody to sell him one. Also, Ilsa, Victor's wife, wanted the letters badly so that they could escape since she knew how important it was to get Victor out of Casablanca so that he could continue his work. To her, Victor's work was more crucial than herself.
On the other hand, the letters of transit were so attractive to some other people such as Ferrari, Ugarte and the theft who killed the two Germans simply because it is literally priceless. Any of them could make a fortune by selling the letters to the highest bidders. Money was what they needed.
To captain Renault, the letters means he could please Strasser, the German officer coming to Casablanca to watch over Victor. Once Renault had the letter, he could assure Strasser that Victor could never escape to America, and that would satisfy Strasser.
To Rick, the letters seemed to be of no importance initially. Yet, it turned out to be his only chance to discover if Ilsa still loved him and why she left him in Paris. After a few times confronting with Rick, Ilsa finally admitted that she still had feelings for Rick, and she left him in Paris to tend to her ill husband when she heard that Victor was alive. We can see clearly how torn she was when she was with Victor. One may realize that her love for Rick is much stronger than that for Victor, yet she understood that she had a responsibility for Victor and his work. If she let her feelings show, she might affect Victor's decision of leaving and that would do no good to the Czech resistance. Thus, she sacrificed her own love and went to Rick for the letters. However, her love for Rick won, and she decided to let Victor go to America while she stayed in Casablanca with Rick.
Rick, after discovering that Ilsa still loved him, decided to let Ilsa go instead of holding her back with him. That was beneficial for Victor and for the Czech resistance that Rick also support, since Victor could escape and continue his work without being affected by Ilsa's decision. "You're part of his work, the thing that keeps him going." That would benefit Ilsa, too, since she would have a better life with Victor than with Rick himself. He said: "Where I'm going, you can't follow. What I've got to do, you can't be any part of." Deep inside, Rick wanted her to stay. But he knew she belonged with Victor. She was Victor's wife anyway.