The purpose of a backsplash is to protect the wall behind your countertop from splashes of oils and other liquids. It also protects the wall from kitchen utensils, cooking operations and even small appliances.
There a lot of options for you backsplash including the same material as you countertop,
tile, stainless steel or any impervious material that can be easily cleaned.
Probably the most common backsplash is the same material as the counter. Even here there are choices. A four inch high splash can often be cut right from the same slab as the counter. If the countertop selection is a granite countertop with a lot of graining or many different shades and colors care should be taken to book match the countertop to the splash. That means the grain or coloring seems to continue from the top up into the splash. This is more difficult and therefore more expensive than simply cutting a four inch strip of the countertop and applying to the wall. Granite that is more uniform such as manmade quartz tops, solid surface materials and even plastic laminates are usually easier because color variation and graining is not as extreme.
A full wall splash from counter to cabinet can also be constructed from the same material as the top. For hard surface materials such as granite and quartz the wall applied material which is made heavy for countertops is very heavy to wall mount. Matching the countertop grain and color for a larger splash is even more difficult – read that expensive. There can also be challenges dealing with the wall outlets which are above every counter.
Full wall tile splashes have a number of benefits including they can add color to the kitchen particularly if you have white cabinets. Tile can also lighten up the kitchen if you have dark cabinets and a dark top and will not need to match the color and grain of the countertop. Tile which comes in smaller pieces will also have less wasted material than materials like granite that come in large slabs. Tile will make it easier to deal with the backsplash thickness at the electrical outlets.