People who are welcoming are extremely friendly and hospitable, like the welcoming family next door that makes you feel right at home in a brand new neighborhood.
When people are welcoming, they're genuinely warm and kind, accepting you into their group. You were nervous to start at a new school, until you met your welcoming classmates. Inanimate things can be welcoming too, like the welcoming scene in your friend's living room when you come in from the cold: a toasty fire in the fireplace and a big plate of chocolate chip cookies. Welcoming is from welcome and its Old English source, wilcuma, "welcome guest."