It's a way to share seeds and acquire new ones. People who participate will receive a box in the mail in a certain order. You can pick out desired seed varieties and then you would contribute seed varieties to make available for others. When done you mail it to the next person in-line on the train. Not all seed trains will have the same rules and qualifications.
Running trains is a good way to get mixed seeds and diseases.
Since the instant gratification/what have you done for me lately explosion in this hobby/industry has come about,there is very little consideration taken when people trade or pump seeds into these trains. A growing majority of people trade seeds for seeds and don't even grow them. As a lover of plants and growing in general,I cannot wrap my head around it.
You would be better off making friends,viewing GLOGS and seeing who is growing clean and true versions and then start trading. Antiquated and boring but way less stress.