What does worshiping God in spirit mean?

Worshiping God in spirit means worshiping Him with our intellect, emotion, and will. Our thoughts, desires, and volition. Not from our flesh; i.e. not in acts of ritual penance, self-flagellation, repetitive/mechanical prayer, and similar acts.

The spiritual part of us (the soul, which contains the spirit) is in the image of God. It is not the essence of God, but in the image. God is Spirit and will be worshiped in spirit.

Jesus boils this worship in the spirit down to love God and love your neighbor as yourself. There is a lot in that. To love God we have to be aware of God, which requires being awake. In real time. In the moment. Especially difficult moments. Then to love our neighbor as ourselves (also put as loving our enemy) we need to intentionally suffer. What Jesus did, allowing Himself to be put on a cross. Jesus, who we are to emulate. Transforming resentment into gratitude, for everything, all the time. Remembering that there is suffering before glory.

So if you are 1.) awake in the moment, aware of God; and then 2.) can transform resentment into gratitude when faced with a difficult thought or event or situation in the moment (resentment is usually targeted at a person or people hence the command to love your enemy); then you are worshiping God in the spirit in the most basic way possible. Engaging or meditating on His word, and also the act of prayer go along with that.