A reputation for hospitality means you're known for being kind and welcoming to visitors, which may also mean that you always have a full house at Thanksgiving.
Hospitalitem is a Latin word meaning "friendliness to guests," so it's not hard to see where the word hospitality comes from. Showing hospitality involves making others feel comfortable and welcome in your home. If you're grumpy and prefer to be left alone, this word probably won't ever be used to describe you, nor are you likely headed for a career in the hospitality industry.
