Hola Robert
I imagine you're referring to these two examples at the beginning of the lesson:
Tengo un libro nuevo y quiero leérmelo pronto.
I have a new book and I want to read it soon.
Tu pelo está larguísimo. Deberías cortártelo.
Your hair is very long. You should have it cut. [lit: should cut it]
The pronouns "me" and "te" are emphatic in these cases, highlighting the intensity of the action. You could omit them and it's still grammatically correct. Here's an advanced lesson on the use of reflexive pronouns for emphasis where you can see other sentences and the nuances. This is called "se aspectual".
I hope it helps.
Saludos
Inma
