Very nicely put in this article from Crisis Magazine, though I would reverse the C’s.
The institutional, big “C” Church is of divine origin, but it has boundaries and edges because it’s run and inhabited by finite humans. It’s like the Basilica itself, which has walls and doors; the liturgy as well, with a beginning, a middle, and an end; there are rules and standards and expectations for those who wish to be a part of these things.
The small “c” church catholic, however, is a mystical body, with boundaries known to God alone. Its membership, unlike the visible Church, isn’t always clear cut. The normal way people attach to that body is through the Sacraments and practicing the Faith, but apparently there are other ways as well—and that’s only God’s business.
In other words, outside the visible Church there’s likely a good deal of invisible church (or at least potential church), but we just don’t always have the eyes to see it—yet. In any case, since we can’t know who’s in the invisible church, those of us inside the visible one have a duty to welcome in everybody, no matter what. Lumen Gentium continues along these lines:
Wherefore to promote the glory of God and procure the salvation of all of these, and mindful of the command of the Lord, “Preach the Gospel to every creature,” the Church fosters the missions with care and attention.
All Christians have a hand in this to be sure, although as laity our preaching can take many forms. Primarily, we preach through our acts of charity and service, through caring for our families and neighbors, through working hard to improve our little corners of the world—living our lives, that is, in a way that always invites rather than excludes. The more we do that, the more we literally extend heaven to those around us, deepening our own interior affinity for heaven in the process.
The irony, of course, is that many of those folks on the outside are already doing this very thing.
Retrieved October 28, 2014 from http://www.crisismagazine.com/2014/extra-ecclesiam-ecclesiam