They grow a new bulb every year, Joanna, from the foliage that the old bulb grew. So the big, pink Mama bulb is a brand-new fresh gladiolus bulb. You can store them for the winter in a cool, dry place and re-plant them next spring.
It's a nice big healthy looking bulb so I'd be very surprised if it doesn't bloom for you next year. Full sun, some fertilizer and enough water, they should do fine, and yes, eventually grow new baby bulbs for you as well from the little cormels.
