What kind of water did Jesus offer to the samaritan woman?

Living water.

We could interprete the living water as Jesus himslf. Jesus Christ is the gift of God, the richest token of God's love, the source and fountain of those living waters, the Holy Spirit which satisfys the thirsting soul and makes a life overflowing with goodness. Those who come face to face with their own helplessness and sin and give their hearts to Him will be the recipients of these living waters.

Or living water could be God's pardoning and justifying grace. His grace quickens sinners dead in sin, and dead in law, and in, their own apprehensions; and causes them to live in themselves, and before God; and because it refreshes and comforts, revives and cheers, and is like rivers of water in a dry land; and because it maintains and supports spiritual life in their souls; and it ever abides, and continues, and springs up unto everlasting life: for the allusion is to spring water, that bubbles up in a fountain, and is ever running.