MHL Cable for Samsung S3/4/5, Note 2/3/4

Can I use this to attach my computer to my tv for watching certain movies & shows?

No. This is the Mobile HD Link cable for the Samsung phones listed.

To connect your computer, it could possibly be as simple as a HDMI cable, it could require additional adapters, or it could not be capable of doing such at all. If you can post the brand, model, and OS, someone might be able to offer suggestions on what you need.