In Eastern culture, the way of expressing great love and continual remembrance is by engraving, which we would call tattooing. This Oriental tradition involved tattooing the names of those you dearly love on your body -- while simply giving gifts to those you love slightly.
Yet God says, "Behold, I have graven thee upon the palms of my
hands . . . ".
God is also saying that it takes too long to look on the arm or the shoulders or across the chest, because that part of the body is almost always clothed with some type of garment. Therefore, God has tattooed us upon the PALMS OF HIS HANDS.
Isn't that a beautiful illustration of God's love for His children? He can see us constantly. He loves us so much that, figuratively, He is willing to bear the excruciating pain of having us tattooed on the palms of His hands because we are dearly beloved of Him. Some apply his engraving his church on the palms of his hands to the wounds in Christ's hands when he was crucified; he will look on the marks of them, and remember those for whom he suffered and died.
John 3: 16 -- For God so loved the world, that He gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.
God is trying to show us how much He cares for us by saying that He has taken a most delicate and sensitive part of His being, and there He has tattooed our names. He doesn't want His love to be hidden underneath any garments or to be covered in any way. At first glance, He wants to be able to see us. That is the love of God. When we understand and see the beauty of these scriptures, we are then able to appreciate the compassion and love of God for us, His children.