You are granted a memento each time to leave a travel location. To view your collection of mementos, go to the Library of Lost Words, and open the bookshelf. You'll see all the mementos you've earned in your travels. (Note that you may have more than 1 bookshelf, and will have to use to left and right arrow buttons to move between them, in order to see all your mementos.)

You can tap on mementos to see information about them, such as what location they came from and on what date your earned them.