What is a typical scenario for using OTRS?
Example: Bob is a manufacturer of VCRs and his customers often have problems programming the VCRs. So they send Bob an e-mail. Sometimes they send a second e-mail to show Bob how important their request is. They are wondering if Bob is alive and how fast he will answer. Bob is using a normal INBOX and reads his e-mails with pine, mutt or whatever e-mail client. Sometimes his two brothers Tim and Joe help him to answer the e-mails. They all use the same INBOX. Of course they have no clue that one customer wrote two e-mails and maybe Tim gives a different answer to the first e-mail than his brother Joe does for the second. So the client gets different information. Of course Bob has no client-history and no clue how much support he is offering. For the next VCR he is producing he has no feedback from his support. That is bad!
But Bob is a smart cookie so he installs OTRS. The e-mail from his customers are not anymore going to his personal INBOX but are routed to the OTRS account (normaly called otrs). The OTRS account has some nifty procmail rules which pipe these e-mail messages to the system. The system answers the client with a standard text which says that they received the e-mail and gives the client a Trouble Ticket Number (which is very important to trace the customers request). The client is happy because he knows that his valuable e-mail was received by Bob and his team. Anybody from Bob's team can open a webbrowser with the URL of the OTRS to have a look at the amount of received e-mails and to answer them. In case the customer Mr. Smith sent a question, Bob can answer it. Maybe Mr. Smith does not understand the question and sends a reply. But Bob is ill. Now even Tim can open this ticket and has access to the history of the ticket. He can read Bob's answer(s) and the original e-mail of Mr. Smith. Tim can answer to Mr. Smith and Mr. Smith even does not realize that he was handled by two different persons.
Of course this is just a very rough overview of the benefits of OTRS. Probably Bob receives some 100 e-mail messages a day which could be handled even without a Trouble Ticket System. But by the time you receive some 100000 or even just some 500 e-mails a day you will be happy to have a system which handles all the e-mails.