Food goes bad and rots with time. In a zombie apocalypse, the electric grid can no longer be counted on to keep the refrigerators running. Add in the difficulties of providing food when civilization breaks down, the ability to make any available food last longer will be of great importance. Over the course of human history, a great deal of ways to preserve food have been invented.
Using the sun or other heat sources to remove water from food. This slow downs bacteria growth which prevents decay. This method is popular on many fruits, fish and meat. Dried meat is also often salted (see below). This method has the advantage of being easy and requiring little resources. An obvious disadavantage is that the food has less water to satisfy thirst. A way to counter that is to dig a hole in hot sand, keep the food there with a bucket in the middle, and seal the hole with waterproof cloth which slopes towards the bucket. It will cause all the water which dries from the food to gather in the bucket. This will provide some water, but this way is not the most effective drying method and you will proabably need to finish drying with other methods.
A way to extend the shelf life of dried meat and fish even further. The food is often smoked alongside this, meaning it is put under a fire, usually fuelled by wood or dried animal dung, and the smoke surronds the food, which improves both ending time and taste.
One of the most popular food preservation methods of the modern day, canning involves cooking food, sealing it in sterile cans, and then boiling the cans. Canned food should be one of the primary targets when scavenging. However, trying to can your own food can be dangerous if not done properly, as dangerous bacteria, such as the deadly botulinium-bacteria, can grow there.
The most commonly used food preservation method of the modern world. However, refrigirators and freezers require a lot of electricity, which is hard to come by in an apocalyptic world.