What is that? Mark Dever explains in the introduction of his book, The Gospel and Personal Evangelism:
What do I mean by a culture of evangelism? I mean an expectation that Christians will share the gospel with others, talk about doing that, pray about it, and regularly plan and work together to help each other evangelize. We want evangelism to be normal— in our own lives and in our churches.
I certainly want that kind of culture in my own heart, and in the church I have the privilege of serving. Dever's little book is a great resource in cultivating an environment of evangelism.
You can read the Foreward, Introduction and Chapter 1 here.