what does what mean?

Billboards are large rectangular structures carrying an image, a poster, a photo.

In 3D, a billboard polygon is a rectangle (or other polygon) that carries a picture and is placed into a 3D scene in order to carry and show that picture without the need for creating a real 3D model version of the same. For example, in a city street scene you could just see yourself texturing a poster image onto a large rextangle that's 'hanging' on a brick wall, to embellish it with today's top news from a newspaper ad, whatever.

More typically, a billboard polygon carries an image with transparency from an alpha channel. That is often used then for realistic foliage, trees, plants, etc... which are either painted (e.g. with PD Particles) or with from Photos that have been worked on to make them stand on transparent backgrounds. So you end up seeing the solid inner side, the plant, and the rest of the scene behind is not hidden by the rectangle's borders.

You can see several examples of plants created in PD Particles at
http://www.thebest3d.com/pdp/tutorials - used in Carrara, Poser, Bryce, Blender and other 3D systems. Doesn't make a difference whether you use PD Particles or Photoshop or Paint Shop Pro or whatever, or whether you buy collections of images like the Xfrog Trees and plants. You can even make your own in a 3D tool like Carrara, and render them with transparent masks or with keying to color later. see for example www.thebest3d.com/carrara/plants
(the first part of it anyway)
I hope this helps understand what a billboard polygon is.

Oh, here's another example, with Carrara:
http://www.thebest3d.com/dogwaffle/whatsnew/3_5/optipustics_new.html
(scroll to the middle and bottom)

-Philip

PS: if you didn't know, XFrog makes image collections of plants