# to equip God's holy people

"to prepare the people he has set apart" or "to provide the believers with what they need"

# for the work of service

"so they can serve others"

# for the building up of the body of Christ

"improvement" or "strengthening". Paul is speaking of people who grow spiritually as if they were doing exercises to increase the strength of their physical bodies. 

# body of Christ

The "body of Christ" refers to all of the individual members of Christ's Church.