Wet brine is a solution of water and/or flavored liquid like juice(s) + salt + sometimes sugar and other spices & flavorings. It soaks into the meat, carrying salt and flavors inside. The salt reacts with the proteins, causing them to trap more moisture in the meat when cooked. The result is moister meat with more flavor.
A dry brine is a mixture of salt and other dry flavor ingredients that are rubbed onto the meat, or in the case of turkey, sometimes under the skin. This process does not add water to the meat, as a wet brine does. But the salt has a similar effect...the salt pulls water from the meat, then the salty/flavored solution gets drawn back into the meat to flavor it, and as with the wet brine, the salt has the same reaction with the proteins, holding in the moisture.
The objection to wet brining is that it takes a large amount of liquid and a large container to store it in, and you've got to keep it below 40*F throughout the brining process. Think "large bucket" taking up lots of space in the fridge (although there are ways to do it in an ice chest outside the fridge). And some people don't like the texture of wet brined meat...the added water can make the meat too spongy for some people's taste.
Lately, I've been doing dry brining with good success. It's sometimes referred to as salting. Here are links to a whole salted turkey and butterflied salted turkeky that I did and liked very much:
Whole Turkey - Salted
Butterflied Turkey - Salted
And a lot more info about wet brining and some brine recipes here:
All About Brining
And several brined turkey recipes I've written about:
Whole Turkey - Basic Brine
Whole Turkey - Apple Brine
Whole Turkey - Honey Brine
Turkey Breast - Bone-In
Good luck!