What are these white lines along my teeth and what are the holes?

Link to my pictures: http://imgur.com/a/zFhht

What did your dentist say they were?

They tell me that the white lines are "cracking" and that I need to keep using SENSODYNE toothpaste for it to be a solid line again. But is it good to have just some random white line?

I don't think it's anything to worry about too much if your dentist has just told you to use Sensodyne. But if you're still worried perhaps you should see another dentist for a second opinion.