A dandy brush is a brush with long, stiff bristles used after a curry comb to get dust and finer dirt off of a horse's coat. Some people also call a dandy brush a body brush or some consider it a soft brush, I find it depends on the person.
A horse's conformation is looking at it's proportions and seeing if they're "correct". Different breeds have different conformations, and different sports have different conformation preferences and deal-breakers.
Lisa Marie explained it better than I did:
What is this course for? Is this the first time you discovered that you were interested in horses?
A dandy brush is a stiff bristled brush used to clean mud and dirt off of the horse's coat. A.k.a a hard brush
A body brush is the same thing except the bristles are softer. A.k.a. A soft brush.
You use a hard brush before you use the soft brush.
And conformation is a term used to described how correct the physical appearance of horse is, as in its proportions and structure. Kinda like what they call "breed standards" for a dogs.
If you're interested in horses, I'd recommend taking a few lessons.