The biblical concept of hospitality is surprising. Unfortunately, we've tamed the concept to mean little more than having friends over. In reality it's a lot more risky. 

Look at its use in the NT: "….contributing to the needs of the saints, practicing hospitality. (Romans 12:13) "Do not neglect to show hospitality to strangers…" (Hebrews 12:2). That word, "hospitality," is actually a compound word in greek. It is a combination of the words philos and xenia. You may recognize philos as "brotherly love." The other word xenia, however, may be a bit trickier. Think xenophobia. Xenia means stranger. 

So, "hospitality" literally means "love for the stranger" in the biblical sense of the word. And, of course, being people of the book, we want the biblical sense to be reflected in how we conduct our daily business. 

Here are some takes on hospitality . . . 

Benevolence done to those outside one’s normal circle of friends.
— Baker Encyclopedia of the Bible
The process of “receiving” outsiders and changing them from strangers to guests.
— HarperCollins Bible Dictionary
The willingness to welcome people into your home who don’t ordinarily belong there.
— John Piper
Inviting the outsider, welcoming unbelievers into our space in hopes of bringing Jesus into theirs.
— David Mathis

Biblical hospitality is the extension of grace to those outside our community. After all, we extend grace because grace has first been extended to us. In fact Jesus uses hospitality as a metaphor for the kingdom of God (Mat 8:11; Lk 14:13). And, why shouldn't he? After all, we were strangers, enemies of God, outside his household, but now we are brought near. It turns out hospitality is a picture of the gospel. 

Two last thoughts. Followers of Jesus are commanded to show hospitality. "Do not neglect to show hospitality to strangers." (Hebrews 12:2)

Also, not having the habit of practicing hospitality disqualifies one from being an overseer. "An overseer, then, must be above reproach, the husband of one wife, temperate, prudent, respectable, hospitable…" (1 Timothy 3:2)