We have several of these plants growing in our garden, but we don't recognize the flower at all. The leaf looks kind of like a lily - long, narrow, with one flower stem. But the "flower pod" that comes out has one flower (approximately 3-4") that lasts for one day; then a few days later, another flower comes out of the same "pod". The one that has bloomed (there are some just budding now) had 4 separate flowers that each bloomed separately and each lasted just one day.
shell flower or tigridia it is a member of the iridaceae or iris family http://www.pacificbulbsociety.org/pbswiki/index.php/Tigridia
Thank you! The name doesn't sound familiar, but I'm sure we purchased it based on the look of the flower, so we must have missed the name of it! Mystery solved!
Add Mexican to shell flower, as in Mexican shell flower and you will have a common name for it that is fairly common.