This is only my own opinion. But I think what is meant here is the immediacy with which a specific datum can be accessed, and how a previous datum can act as the "key" for the next auto-associatively-accessed datum.
So for instance. If you have a list of memory locations in which data is stored, and you want to access a particular datum at a particular index - and you don't know the index, you have to iterate over the list until you find the desired datum - AND - the index of that datum doesn't hold any semantic meaning (other than a location in a sequence), itself.
With "associative" memories, your "keys" can have semantic meaning (be mapped to a "word string" or "sound" etc.) and it will immediately retrieve the desired data without having to iterate over locations or anything!
It is "direct" access and (more importantly), that "directness" is not impacted whatsoever by the amount of data being stored! No matter how much data is being stored, a specific mapping will "go directly" to the datum being accessed.
The above property is critical for large semantic data storages like our brains...