The purpose of Translation Memory eXchange (TMX) is to allow easier transmission of translation memory data between tools and/or translation vendors with little or no loss of critical data during the process.
In Lingo, you can import TMX files from tools such as Trados and memoQ. This lets you leverage all prior translations, whether or not they occurred in the same project or document. By importing a TMX file into Lingo, all of your past translation work will become available as suggestions when you are localizing content in Lingo. Then, when you have finished translating content in Lingo, you can export the TMX files so that they can be used again in the other tools.