Brand association is the connection made in the minds of consumers between a given product or service and the category it is classified in. At its strongest, brand association will lead people to ask for something by brand instead of with the generic name for products in that category. For example, someone might write Kotex® on a grocery list instead of "sanitary napkins." Companies want to build up brand association as much as possible to earn market share.
Products and services can fall into a broad number of categories and it is possible for products to be in more than one category. When companies are developing their brands, they think about how they would like to see their products perceived by consumers. A manufacturer of luxury cars would want people to think not just of "cars" when they see their products, but of "luxury cars" specifically.
In addition to building up associations with particular product categories, brand association also involves associating products with particular attributes. When members of the public want things in specific categories with particular attributes, the goal is to have the brand come to mind rather than to have a consumer look for a generic product. Companies use a variety of marketing techniques to get members of the public associating their products with particular characteristics ranging from "refreshing" for sodas to "reliable" for electronics equipment.
The characteristics people associate with given brands can be a powerful marketing tool. Brand association tends to create a ripple effect, as more and more people are exposed to ideas about products and services. Over time, people who may not have been extensively exposed to advertising may automatically ask for a given brand because they're heard it discussed and been exposed to ideas about the brand. Companies are also careful to control negative aspects of their image as people tend to remember negative impressions of brands and companies.
One issue that can occur with very strong brand association is trademark genericization. If people start repeatedly using a brand name as a generic term for a product or service category and the owner of the brand does not enforce its trademark, it can lose the trademark. Many terms used today as generics, like aspirin, zipper, thermos, and escalator, were once trademarked brand names. Companies walk a line between building strong brand associations and "genericide," as the loss of a trademark through generic usage is known.