Reflexives and Possesion
"Me cepillo los dientes" means I brush my teeth. Why can't you just not use a reflexive and say "Cepillo mis dientes"?
Me cepillo los dientes directly translates to I brush myself the teeth.
2 Answers
Read Daniela's response to my similar question here for an explanation on how the indirect object pronoun functions in these circumstances.
Txustaboy's answer to that question also tells us that your alternative would generally only be heard in literature (thanks Bosque).
The other answers there are also worth reading to gain more knowledge on this type of construction.
In "Panorama, introducción a la lengua española" the authors spend almost a whole lesson on these reflexive constructions. Not only does Spanish does this but the French also.
I tell my students you have to think like this"
I brush myself the teeth. (Me cepillo los dientes.) "I brush my teeth."
I wash myself the face. (Me lavo la cara. ) "I wash my face"
I put on myself the shirt. (Me pongo la camisa.") "I put on my shirt."
I put on/take off (myself) the shoes. (Me pongo/quito los zapatos.) I put on/take off my shoes.
And many others. I demonstrate these using a "Hollywood" Spanish accent, and everybody laughs at me and has a good time. The most important thing is, they never forget it.