Yes, those capsules you see at the daffodil stem tips are seedpods. Many experts recommend removing them so the bulbs have more energy to produce flowers the following year. You can collect this seed, but if it's from a hybrid bulb, the plant that grows from the seed may not look like the parent. If you'd like to create your own daffodil hybrid, you'll need to take pollen from one flower while it's still blooming and place it on the reproductive organ of another flower.
If pollination is successful, the pod should develop after the flower fades. Once the pod ripens and turns brown, break the hard, dry seeds from the pod. Sow them immediately in a sheltered spot in the garden or in a cold frame. Though they'll germinate the following spring, you'll have to wait awhile to see them bloom; it takes most daffodils 5-6 years from seed to bloom.