These are new stem bulblets (below the soil) and bulbils (above the soil). They are basically baby lilies that will be the same as the parent.
In your first photo it looks like you have bulbils on the left and possibly a stem bulblet on the right (with the leaves). For the ones in your second photo, you can see the bulbils have roots. When the main stem start to die back, carefully remove the bulbils from the stem and plant them separately. It will probably take a year or two, but you should get flowers from them as well.