I used them for the first few months. I think they actually prevented the sore, cracked, bleeding nipples that other BF mothers get because they keep the nipple moist and not rubbing against anything. I would apply a small amount of lanolin and put the Lily Padz on under my bra. They "stick" to your skin well and don't move (if you've got them on right).
They do not absorb any milk. I'm not a leaker but sometimes I would get a very small puddle of milk in them. I've read that milk on the nipple is a good thing - maybe why mine didn't get sore.
I'm not sure what the material actually is but they seem silicon-ish.
I stopped using mine because as I started BF in different places (ie: other people's houses, public places, etc.) it got to be a nuisance having to put the Lily Pad somewhere (clean) while BF and then placing it back on discretely (I found you have to have your whole boob exposed to get it on right). Also, I was washing mine once a day (they get a little gunky with the lanolin) and I got tired of doing that as well.
Now, I'm using the Gerber thin BF pads so I can just roll them down (with the bra) when feeding and roll it back up when I'm done.