Mat 25:44 Then shall they also answer him, saying, Lord, when saw we you an hungred, or athirst, or a stranger, or naked, or sick, or in prison, and did not minister to you?
Alternative: And then they shall respond to him saying, "Lord when did we see you hungry, or thirsty, or strange or naked or sickly or imprisoned and did not serve you?

In this verse, all the activities in this parable are grouped under a single term: doing service. Even though the term is used to indicate serving external needs, the focus is on serving the needs of others rather than serving yourself.

This idea goes back to Mat 20:26 (discussed here), where Christ first explains that we become great by doing service. Again, we have to look back to the previous parable about the servants entrusted with money by their master. Those who were the most productive in serving the needs of others were those who were the best rewarded.

The term uses here for "to minister" is first used by Christ as a description of his purpose on earth. His purpose is our purpose. Remember, this sermon started when the Apostles asked about the end of the age, which Christ turned into a discussion of his purpose on earth. That discussion has now come almost full circle, back to his purpose, which is providing service, and our purpose, which is providing, and the final judgment of that service as the measurement of the value of our lives.

"Minister" is from diakoneô (diakoneo), which means "to minister," "to do service," and "to render a service." From diakonia, which means "service," "attendence to duty," and "ministering to external wants" and diakonos, which means "servant" and as an adjective, "servile" and "menial." In Christ's period, this later term was also used to indicate an attendant or official at a temple. It is the source word for the English term "deacon."