Druids are the one class in the World of Warcraft that can take on a variety of forms. Sure, the Shaman has her wolf forms, but your Druid forms amount to so much more. Your various forms can run, swim, fly, do massive damage, and so on. This shapeshifting is one of the things that makes the Druid so very versatile and effective in any aspect of the game.
Of course, if you're going to use all of the Druidic forms well you're going to have to put in some effort. The class is a little harder than others because of this same flexibility.
So what are these forms?
So let's do a run down of the various Druid forms that are available to you and what they're all about.
First off is your "Caster Form." This is what you start with as a brand new character and, for a few levels, it's all you will have. It's the same as everyone else gets, too. You will be just your basic Night Elf, Worgen, Troll, or Tauren and you'll be throwing the "Wrath" spell around a lot.
Cat form come at level 6 and is where you can really start doing some damage. Of all the Druid's various forms this is the one that does the most damage, right up close and personal.
Bear form, at level 8, can also do some damage, but that isn't the Bear's main forte. Survival is, and when you hit level 10 you can pick the "Guardian" specialization (spec.) The Guardian is a "Tank," which just means that in dungeons and raids you get to be the center of attention and your job is to keep the attention of all the enemies in the immediate area. See what I meant by Survival. You will never do as much damage as the Cat, but you will last a lot longer.
Travel form, at level 16, is a nice speed increase. You take the form of a Stag, antlers and all, and trot right along at the same speed as a basic mount. If you prefer the old Travel Form (prior to Mists of Pandaria) you can get a Glyph of the Cheetah.
Aquatic form, level 18 - kinda like SCUBA diving, now you can explore all those underwater places and swim around at a decent speed. The Glyph of Aquatic Form lets you swim even faster.
Moonkin, at level 29 - This form requires the "Balance" spec and if you aren't Balanced you can't do the Boomkin thing. Balance is the Druid's version of the Mage, you stay at range and lob damage at the opposition as opposed to doing it "face to face."
Flight form, acquired at level 58, allows access to all those high places in the Outlands. You will have to wait until level 60 and then get a Flight Master's License from your home city to be able to fly in the lands of Azeroth. Cold Weather Flying will be necessary to fly in Northrend and you have to wait till 90 to fly in Pandaria.
Epic flight form, at level 70, allows you to reach those high places even faster. You can keep the same licenses as before, you're just faster now.
Glyph of the Treant teaches you the Tree Form. This used to be the form that Druid healers (restoration) would take, but now it's optional. One advantage to the Tree, besides role-playing, is that you stand out in a group. Your team can more easily find you and aid you, such as in PvP or a raid.
One of the additional cool things about shapeshifting is that it allows you to immediately pop out of "Movement Impairing Effects." If some player or other enemy slows you, for example, you can shift forms and immediately escape. Sometimes you can also escape from other effects. This is a very nice ability to have in PvP.
Lastly, just because you can shift to various animal forms it doesn't mean that you can talk to them. They'll treat you just as if you were any other class and will take no note of your awesomeness.