Devoir and Falloir can be confusing because they both express obligation and necessity, but in different ways. In addition, each verb has a different meaning when followed by a noun.
Devoir - When followed by an infinitive, devoir expresses obligation, probability, or supposition.
Je dois partir
I have to, I must, I'm supposed to leave
Falloir - stronger and somewhat more formal than devoir; it expresses necessity. Falloir can be used with an infinitive or the subjunctive.
Il faut travailler
It is necessary to work, One needs to work.