Wow, and here I was thinking it was so strange that the OP said people didn't really know about banana pudding!
There are lots of variations but all the ones I've had have had a vanilla pudding base, sliced bananas and something like vanilla wafers. Sometimes those are layered together, other times they are just mixed up together. Sometimes it has meringue or whipped cream on it, sometimes it has brown sugar in it, sometimes people change it in other little ways. It's really popular in the south - you can find it all over the place. The best ones have homemade pudding or at least "cook and serve" pudding. It isn't nearly as good if you use instant pudding.
Ahh, that does sound good. It is sort of like a banana cream pie that I make - graham cracker or chocolate wafer crust/sliced bananas/pudding/whipped cream. For added decadence, I sometimes line the crust with dulche de leche before layering in the sliced bananas.
I was thinking that banana pudding was just banana flavoured pudding - and I would have been one of those who said "no thanks!". This sounds tasty.