What is the name of the tissue that attaches the muscle to move the bone?

It's a tendon.

These 2 links should help you.

Introductory Anatomy: Muscles & Nerves (http://www.leeds.ac.uk/chb/lectures/anatomy5.html)

New Page 2 (http://bioe.eng.utoledo.edu/adms_staffs/akkus/4740_2004_WEB/tendon/tendon%20web%20page/anatomy.htm)