There is something to be said for the headspace something like a collar or cuffs etc. will put a sub in. All the answers above are spot on, so I won't repeat what has already been said about the mental reaction to a symbol such as a collar.

I will add that, for me, the physical sensation of being securely "held" also adds to that feeling of calm and safety you describe. I often sleep in my collar simply because the feeling of being firmly held on to soothes me and puts me in a secure and peaceful frame of mind.

If you have ever experienced more advanced rope bondage, a karada for example, you'll find that the snugness of the ropes on and around your body will give you an even more complete feeling of being held and wrapped up safely. Even as you move and even when your Dom is not in direct contact with you, it's as if you're being cradled in his arms.