These words come from the well known Psalm 23 that starts with: The Lord is my Shepherd
From this Psalm we know that our Shepherd Jesus:

takes care of us everyday; guides us along the right paths; were willing to lay down His life for His sheep; gives us everything that we need; are close beside us - always; leads us to a quiet place where we can rest and be refreshed and renewed; protects us; comforts us; heals us; pours out His goodness and unfailing love on us, over and over again.

THE CUP OF SORROWS

When Jesus died on the cross, He emptied the cup of sorrows, the cup of suffering, in our place. In Matt 26:39 He prayed in the garden of Gethsemane: My Father, if it is possible, take this cup of suffering from Me. Yet, not what I want, but what You want. He drank the cup of suffering and pain to the end, and died with the words: It is finished (John 19:30).

.THE CUP OF SUFFERING IS TURNED INTO A CUP OF BLESSING

By His grace and through His faithfulness, Christ has turned that cup of suffering into a cup of blessing, which now overflows for each and every one of us.

We know for sure that our grief is turned into wonderful joy; we rejoice and no one can rob us from that joy (John 16:20) ... our cup is overflowing with blessings! You have changed my sadness into a joyful dance; You have taken away my sorrow and surrounded me with joy. (Ps 30:11); Tears may flow in the night, but joy comes in the morning. (Ps 30:5)

We receive from Him: flowers in place of sorrow, olive oil in place of tears, and joyous praise in place of broken hearts; a crown of beauty in place of ashes, joyous blessing in place of mourning. (see Isa 61:3)

THE CUP OF ABUNDANCE

Jesus said, I came that they might have life, and might have it abundantly (John 10:10). That is a cup running over with Gods grace. Jesus gives us Himself (John 14:6). He IS this abundant life for us.

My cup overflows, means it is not just full; it is running over, filled to the brim and overflowing. Gods saving grace is always like that. His grace is always in fullness, abundance and all-sufficiency. We are drenched with His goodness and that should satisfy us completely.