Backerboard is a fiber- and cement-based material that is commonly used under tile floors or walls, particularly in rooms that encounter moisture, such as the kitchen or bathroom. The main benefit of backerboard is that it is waterproof, which can save time and money if water seeps through the tile. Other materials -- even water-resistant greenboard -- can be damaged by excessive amounts of water, which would require the affected area of the wall to be cut out and replaced.
The wall you choose to highlight will determine whether you should use backerboard or not. If you are using the backsplash area of the wall behind the sink as your accent wall, backerboard is a good idea, though not necessary. It is possible to install tiles or paint the wall without backerboard, though you will run the risk of water damage. Alternatively, backerboard would not provide any benefit if your accent wall is opposite the sink and away from any water.
Backerboard can serve as a sturdy and convenient material under tile if you plan to use tile on your accent wall. Tile can also be installed on drywall, which may be easier and less expensive if the accent wall does not back up to a sink or other water source. Paint or wallpaper works well over regular drywall. Do not install backerboard on the accent wall if you plan to paint as you cannot paint backerboard.
Your accent wall should immediately command attention when you walk into your kitchen, establishing the look and feel of the room. Use the wall that you first see when entering the kitchen, unless a different wall makes more sense. Colorful tiles, a pattern or rich, warm colors can instantly transform your kitchen into an inviting place. Tie the color or pattern of the accent wall into other areas in the kitchen by using the same colors or images on towels, small appliances and decorative items.