In the brain, there are trillions of synaptic connections that exist between billions of neurons. The synapse is the point where one neurone connects with another so that a charge can be transmitted between them. Memories are neurological realities, pathways in the mind of connected neurons. Memories are triggered when a part of the network they are associated to is triggered. The network of memories is called an associative network.
A brand (and every other concept) is made up of a network of associations. The essential purpose of marketing is to shape the network of associations in the consumer's mind so that it connects the brand to things that are at some level significant and relevant to the consumer at psychological level.
The most famous example of this was the way Coke forged an association with Santa and thereby connected with the anticipation and joy the population associate with Christmas.