The Brush tool draws brushlike strokes, as if you were
painting. It lets you create special effects, including calligraphic effects.
Unlike the Pencil tool, the Brush
tool draws both a fill and an outline.
You can press the Shift key while dragging to constrain
drawing to vertical or horizontal directions.
You can specify the Brush Mode in order to define the
way the tool works:

Also, in the Brush options, there is a drop down that
lets you select the size of the brush. Simply click the size you want.
Finally, the Brush options lets you select the shape
of the brush. Try experimenting with the different shapes and see what effect
each offers.
The last option listed under Brush options, is
the Lock Fill option. The explanation for this is a bit tricky.
When you use the brush tool in it's default state
this option is not turned on. Let's assume that you selected a gradient fill
and painted something using the brush tool. In this case the brush tool would
use the center of your painting as the center for the gradient fill.
Now, if you paint yet another drawing next to the
first one, Flash will use the new drawing's center as center for the gradient
fill.
However, had you pressed the "Lock Fill" option
before drawing the second painting, Flash will maintain the gradient center
from the first painting.
The best way to understand this option is trial and error,
so if you don't get the above explanation, then try painting with and without
the "Lock Fill" option set. While doing so, make sure that you use a gradient
fill for the drawing or you won't see any effect at all (because plain colored
fills have no center).