The romantic scene at which your question arises is when the couple is coming up out of a wilderness to the place that was the woman's home, near a fruitful apple tree. She come up with her arm in his and her head in his chest.
She never wants this posture to end, that is under his protective care, so she imagines herself forever like this by having her image and likeness pressed upon a signet ring seal. The 'seal' in Greek is a signet ring. These were wrapped around the arm, on the hand or on a necklace.
The seal represent ownership and security, for when stamped on a message on wax, when un-broken it authenticated the message of the sender. Not only so but this seal would always be before the eyes and heart of the owner.
The symbolism seems straight forward then, even though the commentaries disperse in many directions amd with some valid difficulties. She wants to posses her husband and never let him go. She want his possession and signature to be her. She wants their love never to be broken or tampered with.
She is the church that was born in a fruitful land, he is Christ the redeemer who brought her out of a wilderness. The person speaking is the woman, the church.
The only reason why there is some difficulty here is that in the previous verse many disagree who is speaking but it seems more reasonable that it is the man who awakened the woman's love, earlier under that tree. Some think the church awoke Christ's love in her prayers, but it makes more sense to me that Christ awoke the bride. Possibly the man literally awoke her once before as she rested in its shade, possibly he declared his love to her on that very spot. Maybe both.