Each time you place a tile, your little figure guy draws the longest path he can from his current location to the new tile, so as to maximize the points you get from his journey. Normally, when drawing his path, the figure can never step on the same tile more than once per path. However, with "Home", yellow "Indulgence" tiles can be stepped on more than once.
If you have more than one "Indulgence" tile next to each other, "Home" allows your figure to walk back and forth between them to rack up a bunch of points!