Well, in the program I use (though these terms most likely apply to all art programs), brush strokes are repeated movements of the brush tool on an area. Basically, it's just coloring over an area. In this case, you could color over the parts of its fire where the letters still exist and make it look like they were never there.
A soft eraser is just the eraser tool with its hardness decreased. With the eraser tool softened like that, using it on the outline makes the edges less defined, and normally makes the render a little better (depending on the effect you're going for).