Basil doesn't make seed pods. The seeds are nestled in the remnants of the dried up flower head. The seeds are dark, small, round to oval in shape.
If you like the basil you grew, you can definitely grow them from seed. Most Basil(might be all, don't have time to look it up right now) is not hybrid. If you want to have more plants, it is worth it. If you only want one and want to spend the few dollars on a new plant, you can do that too.
Remy

I bought some basil plants this spring at the nursery, and I also got some seed. The seed I planted was unbelievably easy to germinate, it was lime and a purple basil. I don't even think I watered it much and they sprouted into strong little plants.

I'm missing those plants right now, as I pulled the dried herbs from my cabinet to make sauce tonight...

I know I can wait a few months and get another plant for a few dollars, but I'm in experimentation mode. And my garden is so small (1 4x4 square foot garden bed for now, plus a few pots) that it seems silly to buy a whole packet of seeds when I'm only going to have 2 or 3 plants. So I thought I'd ask. I guess I can give it a try with one of the indoor plants I have, and see how it goes!