The word "long" conveys a sense of intense longing and a strong emotional need for physical closeness and affection. It suggests that the person's desire for their embrace is profound and meaningful.
The phrase "for your embrace" specifically indicates that it's not just any embrace but the embrace of a particular person that is craved. It emphasizes the unique connection and comfort that this person's embrace provides.
In essence, this statement beautifully captures the idea of seeking solace, warmth, and emotional connection through the physical act of being embraced by someone they care deeply about. It's a poetic expression of the need for the comfort and security that love and physical closeness can provide.