The value in sending thank you letters in the business setting is that this practice is a good way to build and improve relationships with people with whom you do business. Thank you letters are not essential and not a panacea, but they are a relatively simple and easy way to help build relationships.
The main point of a thank you letter is that it shows that you appreciate something that another person has done for you. You might appreciate them making a large purchase from you. You might appreciate them taking the time to interview you for a job. By writing them a thank you letter, you express that appreciation and let them know that you noticed the effort they made on your behalf or the benefit that their actions had for you.
This is an important thing to do because people naturally like to feel appreciated. People are much more likely to want to do things for those who appreciate them. Therefore, sending a thank you letter is an excellent way to build a relationship and to make it more likely that people will want to continue to do business with you.