Souvenirs are mementos that your character keeps after completing various Story Arcs. There is no physical representation of them in the game. To view Souvenirs that your character has obtained, open the clues window and then select the souvenirs tab. You can then expand each souvenir to recall the story of how you obtained them.
Before Issue 11, a character was restricted to only 100 souvenirs before their tab just wouldn't take anymore. With the new change, this limit was bumped up to 250.
The souvenir system has been in game since City of Heroes first came out, but it has always been one of the game's half unfinished sections. The images of each souvenir were never added and still have only the placeholder question mark image, and several bugs involving Task Force souvenirs lead to them being removed from the game as a whole, preventing anyone from receiving them.
As of Issue 11, many of the hero side Task Force souvenirs have been reinstated, while those TFs made during the missing period lacking in them. Additionally, the villain equivalent of Task Forces, Strike Forces, are still lacking.