When the Buddha was alive, the ability to sit on the floor was very common because a lot of households had no chairs. People ate on the floor, and when the monks and nuns went wandering from town to town, it was very convenient for them to not have to carry a chair or other such things with them, so they sat on the ground.
The lotus posture, whether it's full-lotus or half-lotus, came about because most people were very comfortable in that posture in those days. It's more difficult today, because people are not as used to it, especially Westerners. Most of you haven't even tried these postures until you were an adult, so it's more difficult to get the flexibility involved to sit in these positions.
From my understanding, as far as the formal posture goes, the benefit of being able to sit full-lotus is that it's harder to fall asleep. Sitting in the half-lotus makes it a bit harder to fall asleep, but not quite as hard as when sitting in the full-lotus. Interesting? I'll show you why. If I'm just sitting here with the legs in front, and I'm falling asleep, I can fall any which way I want. Hey, it's easy, I can fall over any way which I want. The moment I sit half-lotus, it's harder to fall in one direction. One way is easy, the other way is not. When I sit full-lotus, it's very hard to fall either way, because I'm tied up in a kind of little knot, and it is just harder to fall over. The posture itself actually does keep people more awake.
However, as I've said, and as I've said often, the full-lotus posture is very hard for most people. Don't worry if you can't do it, because most Thai people can't do it either. Many of you, most of you perhaps, can sit half-lotus if you try hard enough. For some people it takes a few years to get stretched out enough. The ankles have to stretch, the knees have to stretch, the hips have to stretch, the lower back has the get stronger, it takes some effort for some people. Some other people are very natural, the minute they sit down, they flip the legs up and they're fine. But that is not as common as when people have to work at it.
As you've heard me say before though, what you do inside is more important than what you do outside. So if you can sit full-lotus or half-lotus, that's fine, depending on what you do inside. If you sit cross-legged or on a bench or chair, that's fine, too, depending on what you do inside.