"The head is not more native to the heart" is the first part of an analogy that King Claudius makes between himself and Polonius, his counselor and father of Laertes. This comparative situation suggests the closeness of the mind to the emotions, and how they work together. That is, Polonius's mind and his ideas relate closely to what is in the heart of King Claudius.

In order to understand the meaning of this quote, it is really necessary to include the rest of the comparison:

The head is not more native to the heart,
The hand more instrumental to the mouth,
Than is the throne of Denmark to thy father.
What wouldst thou have, Laertes? (1.2.47-50)

Extracted from Act I, Scene 2 of Hamlet, this line is part of a conversation of King Claudius with Laertes, the son of Polonius, who is Lord Chamberlain and a conniving sycophant to the king, who is equally despicable. Laertes has returned from France on the bequest of his father in order to be present for the coronation of King Claudius. Since his filial duty has now been served, Laertes wishes to return to his school in France, and so he comes to ask the king for permission to do so. Evidently, Laertes seems to be timorous before the new king; therefore, Claudius tries to allay his fears with the two lines that demonstrate his close relationship with Laertes's father.

 In the lines cited above, Claudius makes an analogy between the strong connection of the head to the heart/mind to the emotions, and the hand to the mouth and his close and mutually satisfactory relationship with Laertes's father. Polonius, King Cladius's advisor=the head to the king's heart--"the head is native, or relates, to the heart." 
(Later, the reader learns it is Polonius who devises some of the plots to learn what is in Hamlet's mind.)