If you subscribe to something, you sign up to receive it regularly. If you subscribe to the New York Times, it's delivered to your door every morning or you get online access.
When you subscribe to a belief, you adopt it as your own. You might subscribe to the notion that children should be seen and not heard, or you might wholeheartedly subscribe to your town's proposal to save the wetlands. A less common use of subscribe is to sign your name on something, reflecting the origin of the word, which comes from the Latin subscribere, "to write below," that is, to sign at the bottom of a document.