Romans 12:6-8 meaning

God has gifted us all in different ways, we have gifts that differ according to the grace given to us (v 6), we are each unique in our abilities. Here, Paul is talking about our spiritual gifting; these are abilities God has given us to serve other believers (the Church) sacrificially (v 1) and each of us is to exercise them accordingly (v 6). 

The Greek word "charis" translated grace in v 6 means "favor." Context determines who is granting favor and for what reason. An example is in Luke 2:52, where Jesus grew in "favor" ("charis") with God as well as with people. We can presume God was mainly looking at Jesus's heart and the people were looking at His behavior, but each decided what Jesus was doing was favorable. 

God has given each of us the grace ("favor") of granting us the capabilities and opportunities we have. And He tells us that He will judge us according to what we do with the talents and opportunities we have (Matthew 25:21; Luke 12:48). The corollary to this would be that God will not judge us for talents or opportunities we do not have. Therefore, it behooves us to be faithful wherever we are with whatever we have rather than claiming that we would be faithful in some other circumstance. 

Paul goes through a short list of different gifts. If we have the gift of prophecy (truth-telling, preaching) we should use that gift according to the proportion of faith (v 6), and if service, in his serving, and if teaching, in his teaching (v 7). Or he who exhorts (encouraging), in his exhortation; he who gives, with liberality; he who leads, with diligence; he who shows mercy, with cheerfulness (v 8). 

The emphasis is on applying gifts we have into opportunities we are provided. We should use our personal gifting to serve one another. To use Paul's analogy of a body, if we are a foot we should not attempt to be an eye—we must have humility (see reality) to know what God has given us and how we ought to use it.

For many of us, it is difficult to "see with reality" (i.e. humbly) what our gifts are. We tend to depreciate what comes easy for us, thinking "That is so easy, anyone can do that." The reality is, however, that what is easy for us is often very difficult for others. Something that comes easily to us is often because we are gifted in that arena. It is our job to reach a level of self-awareness regarding our gifts, so we can employ them effectively in service to others, so we become a living sacrifice in our daily lives. Becoming a living sacrifice is the logical way to live, given all that Paul sets forth in Chapters 1-11 (Romans 12:1). 

When applied, each person's gifts interact to create a healthy and harmonious body. We need 

• prophets to sort out what is true and guide us to make wise choices, 
• teachers to teach us God's word so we can renew our minds, 
• people to encourage us throughout our life so we can persevere, 
• generous members to help provide for the needs of others, 
• leaders who are hard-working and diligent, and 
• merciful people to show empathy and personal care. 

This partial list of different members and different gifts demonstrates how living harmoniously with each other is built upon using what God has given us for the benefit of each other, sacrificially and humbly.

This listing of gifts is not intended to be limiting, but instructional. The main point is to "discover how God has empowered you and use those gifts diligently and enthusiastically."