This is a word used to express the character that should be displayed by believers in Jesus Christ. So in Philippians 2:15 we read that you may be blameless and innocent, children of God without blemish in the midst of a crooked and twisted generation, among whom you shine as lights in the world. This idea behind the word blameless is that the christian is to be without reproach. There is nothing in our lives which blemishes our reputation. It speaks of reasonableness and honesty.
It is especially to be so of those who are called to eldership in the church that they are blameless. When the qualifications for eldership are examined in 1 Timothy 3 we see that they start with: an overseer must be above reproach (1 Tim. 3:2a). This is the headline quality that an elder should have. In the church and in the community he should be known for the quality and consistency of his godliness. The rest of the qualifications stated in 1 timothy 3:2b-7 really explain what it is to be without reproach.
There are many good things to aspire to in life. However, for a Christian this must take priority. We need to aspire to being blameless. This is not a glamorous quality in the world and often it is not appreciated in the church. But with God it is well-approved of.
And may we be seeing many many rising up to shine out with their blamelessness so that they can be elders who can shepherd the flock of God.
When we see this attribute emerging we will be seeing more of our Lord Jesus in the church through the characters of His people. He is after all the ultimate blameless one. And as Robert Murray McCheybe said: It is not great talents God blesses so much as great likeness to Jesus.