What actually are thoughts?
The hippocampus helps to solidify the pattern of connections that form a memory but the memory itself depends on the solidification of connections between the individual brain cells". 


This refers to the phenomenon called Long Term Potentiation which regulates synaptic strength between neurons. Certain patterns of firing (high frequency) causes the post synaptic neuron to strengthen the synapses. One way of doing that is by increasing the number of receptors (Usually NMDA receptors). Due to this, the response would be stronger in the next firing event. You can imagine its effects- more number of times you read a passage better will you remember it. 

Hippocampus is involved in this process (it is one region where a lot of synaptic dynamics happens) but consolidation and long term storage of memories is handled by the cortex. Essentially what happens when a memory is formed is strengthening of synapses.