The grammar can be broken down this way:
Oh / you / will not bring / (to) me / all the things (that) I need?
Oh - interjection, expressing intense emotion, in this case, desire.
you - subject
will not bring - verb
me - indirect object
all the things that I need - direct object phrase
It is phrased as a question, and as a longing, for the person to do something. When someone asks a question like "Will you not...." it is meant to goad the other person into action, and as @Astralbee has pointed out, to remind the other person that he/she is currently not doing that.
The singer is asking for the person (you) to "bring them all the things that I need" -- meaning take care of all their wants and needs.
This is a common way of thinking -- that another person can completely satisfy another person, by providing for all of their wants and needs. You see it expressed in fairy tales, romantic movies, and so on. It is not meant literally, but rather as a romantic expression.