Without a doubt serving Christ requires us to DO things. If we are to be the hands and feet of Jesus to people, we will be physically active in many of those instances. But it goes even deeper than that to the point that serving Jesus is more about who we are than what we do. When we start to mature as a child of God, in Christ, the serving part is just a natural component of who we are.
If we are living righteously (which only comes through the blood of Christ), then He is our life. He is the One we serve. We strive not only to be like Him and to 'be Him', serving people as He would if He were physically here but doing it in His name out of love for both Christ and people, yet in service to Him. Yes, people receive the end result of our service, but the best service they can receive from us comes out of our motivation to serve Jesus.
So what does that look like?
"I was hungry. And you gave me something to eat. I was thirsty. And you gave me something to drink. I was a stranger. And you invited me in. I needed clothes. And you gave them to me. I was sick. And you took care of me. I was in prison. And you came to visit me.’ “Then the people who have done what is right will answer him. ‘Lord,’ they will ask, ‘when did we see you hungry and feed you? When did we see you thirsty and give you something to drink? When did we see you as a stranger and invite you in? When did we see you needing clothes and give them to you? When did we see you sick or in prison and go to visit you?’"(Matt 25:35-39)
Jesus' answer to their question should sink deep into our souls as we learn to serve.
“The King will reply, ‘What I’m about to tell you is true. Anything you did for one of the least important of these brothers and sisters of mine, you did for me.’" (Matt 25:40)