A website needs to be useful, relevant and well-designed. This can be accomplished with compelling layout design, balanced use of color, good organization, ease of use and functionality.
According to a recent study mobile usage in the US has surpassed the desktop, so a responsive design that adapts to mobile devices is important. A desktop homepage can serve many purposes, but in mobile the user should be able to get to the content easily. Remember to set the viewport and use CSS media queries for a flexible layout with appropriate breakpoints.