When you're neighborly, you are friendly and helpful to the people who live in your neighborhood or building. A neighborly (and backbreaking) gesture might be shoveling the snow on your neighbor's driveway.
It's neighborly to say hello to people who live nearby, and it's also neighborly to organize a block party and invite everyone on your street. It's less neighborly to leave your barking dog tied up all night right outside your neighbors' bedroom window, or to have loud parties without inviting your downstairs neighbor. Neighborlike was once more commonly used than neighborly, and both come from Old English roots, neah, "near," and gebur, "dweller."