Restore in the original Greek language is katartizo. It means to render, to fit, to make sound, or to complete. It is also used to describe fishermen mending their nets. In the context of Galatians 6:1, Paul is explaining that we are to mend or to make sound those who have fallen. This must be done in a spirit of gentleness and humility.
I sometimes wonder why there seems to be so much condemnation within the church from those who claim to be "spiritual." Personally, I was raised in a fear based Christian context where punishment ruled over grace. Yet, clearly Paul states that those who fall should be put back together and restored in grace and humility by those who are able to look at themselves and understand that they are no better than the person who is currently struggling.
I feel that all believers should heed Paul's words here. Restoration is vital to building up the body of Christ and we all need to be able to gently help people who stumble because we all will stumble at some point.