Textures will come in .zip packages, those .zip packages go into your texturepack folder. The "open folder" button is there just to give you easier access to the folder so you can drop new .zips in. If you don't see any other texture packs in the in-game selector then you don't have a pack to load.
The Mapping&Modding section has many packages you can use, highly suggest taking a look around there (viewtopic.php?f=25&t=12352 is a good start)for some. There's probably much better instructions and help in there than what I just rambled.
I believe the file structure within the .zip is important, not all packs are up to date. Also, if you're using winrar to do your zipping you should check to make sure it's actually a .zip and not a .rar, minecraft won't recognize it and they'll have the same icon.
Other than that, I'm not sure, as long as the .zip is there and everything inside it is in order then it shouldn't be having issues.