What is the scientific basis of associative memory?

We don’t know how memories are stored let alone how they associate. Neuroscience is fairly young. It has made a lot of interesting discoveries, but it has a long way to go. Figuring out the organization of billions neurons is no small task.

I second what @LostInParadise said – nobody has a clue how human memory really works at any level, including molecular, despite all the research. Interestingly there’s an analog in silicon hardware known as content-addressable memory, which of course is nothing like the wetware inside our heads!

Our brain stores what is known as “frames of reference”. The imagery for that would be like a long string leading to the memory. If we base other important events on this memory without even thinking about it we add another string or map to this. Thereby strengthening this memory. A key event or word, smell or other taps into this mind map or frame of reference and restores a memory. Or associative words, smells etc., Also memory recall strengthens a memory. Also the memory is only as old as its last recall.

Donald O. Hebb, a pioneer in neuroscience proposed Hebb’s Postulate (1949). http://www.ncbi.nlm.nih.gov/pubmed/11283308 offers a updated version of Hebb’s Rule.
Hebb was one of my Intro Psych professors at McGill in 1971. I took courses from several of his research colleagues including Peter Milner and Ronald Melzack. Looking back, I can’t believe my good fortune back then!