To achieve a Walk-Off home run, the home team bats in the bottom half of the 9th inning or the bottom half of extra innings should the score be tied at the end of the regulation play.
The home team batter hits a home run to score the go-ahead run to win the game because the visiting team does not have another change to bat. The individual does not walk around the bases but jogs touching each base as he passes it. Usually there is a celebratory group of home team players waiting for him at home plate to congratulate his achievement. The term "walk-off-home-run" comes from the fact that now everyone walks off the field because the game is over.
Of course, a walk-off hit can achieve the same win but this is not a walk-off home run. In this case, other home team players are already on base and the hit allows one of the players to score a run to win. Still everyone walks off the field because the game is over.